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"A  Graduated  Scale  for  Determining  Mental  Age' 


BY 


CLARE  BROWN  CORNELL 


A  Thesis 


Presented  to  the  Faculty  of  The  Graduate  College  in  the 

University  of  Nebraska  in  Partial  Fulfillment  of 

Requirements  for  the  Degree  of  Doctor 

of  Philosophy 


Department  of  Philosophy 

Lincoln,  Nebraska 

1915 


_,\ 

•vx 


Publishers 

STATE  JOURNAL  CO. 
Frankfort,  Ky. 


Copyright  1918  by 
Clare  Brown  Cornell 


Acknowledgments. 

In  working  out  a  problem  which  has  as  its  basic  material 
the  measuring  of  human  intelligence  one  is  quickly  brought  to 
feel  his  absolute  dependence  on  his  fellows.  In  art,  in  the  other 
fields  of  science,  in  literature,  given  a  well  equipped  laboratory, 
or  a  shelf  of  carefully  selected  books  and  periodicals,  the  task 
of  working  out  an  investigation  becomes  one  of  cataloging  and 
classifying  known  facts  and  of  establishing  new  ones.  But  in 
the  field  of  psychology  the  investigator  is  peculiarly  helpless 
unless  he  can  secure  the  intelligent  co-operation  of  people  who 
see  the  value  of  his  work.  The  author  of  this  monograph  was 
especially  fortunate  in  this  respect,  and  wishes  to  take  this  op- 
portunity of  expressing  his  appreciation  of  the  assistance  given 
him  by  the  teaching  force  of  the  Lincoln  (Nebr.)  Public  Schools. 
Thanks  are  particularly  due  to  Superintendent  Fred  M.  Hunter, 
who  gave  him  the  freedom  of  the  entire  system ;  and  to  the  prin- 
cipals of  the  eight  schools  from  which  the  children  were  selected, 
namely,  E.  Ruth  Pyrtle,  principal  of  McKinley  School,  Lena 
Merrill,  principal  of  Saratoge  School,  Emma  Morrill,  principal 
of  Everett  School,  Mattie  Allen,  principal  of  Whittier  School, 
J.  Belle  Corbin,  principal  of  Bancroft  School,  Clare  McPhee, 
principal  of  Capitol  School,  Bertha  K.  Green,  principal  of 
Clinton  School,  and  Sadie  Baird,  principal  of  Elliott  School. 

The  author  is  greatly  indebted  to  Dr.  H.  K.  Wolfe,  head  of 
the  Department  of  Psychology  in  the  University  of  Nebraska, 
who  suggested  and  directed  the  investigation,  and  to  Dr.  Wini- 
fred Hyde  for  helpful  criticisms  during  the  process  of  arrang- 
ing the  material. 

The  Author. 
Lincoln,  Nebr.,  July  20,  1915. 


After  carefully  checking  the  data  and  after  using  the  scale 
in  a  large  number  of  cases  covering  a  period  of  three  years,  the 
author  feels  justified  in  presenting  the  work  in  its  complete 
form.  The  results  obtained  by  the  use  of  the  scale  are  accurate 
to  a  marked  degree.  Correlation  of  the  individual  tests  with 
results  obtained  by  the  Binet  scale  are  decidedly  close. 

C  B  C 
Lexington,  Ky.,  July  10,  1918. 

417953 


A  Graduated  Scale  For  Determining 
Mental  Age. 

Introduction. 

HE  science  of  mental  measurement  is  a  logical  out- 
growth of  experimental  psychology  and  can  be 
traced  indirectly  to  Fechner  and  Wundt.  Al- 
though based  upon  seemingly  intangible  psychic 
phenomena,  its  methods  nevertheless  parallel 
those  of  the  other  sciences.  There  is  this 
difference,  however,  between  the  two  fields: 
in  the  other  sciences  definite  units  of  measurement  have 
been  established  and  generally  accepted,  whereas  in  the  science 
of  mental  measurement,  very  few  standard  units  have  as  yet 
been  fully  developed,  owing  to  the  peculiar  difficulties  inherent 
in  any  attempt  to  determine  the  required  norms.  "The  problem 
for  quantitative  study  of  the  mental  sciences  is  to  devise  means 
of  measuring  things,  differences,  changes  and  relationships  for 
which  standard  units  of  amount  are  often  not  at  hand,  which 
are  variable,  and  so  unexpressible  in  any  case  by  a  single  figure, 
and  which  are  so  complex,  that  to  represent  any  one  of  them  a 
long  statement  in  terms  of  different  sorts  of  quantities  is  com- 
monly needed,  "t25'6)  But  in  spite  of  the  difficulties  encountered 
a  relative  degree  of  success  has  attended  the  search  for  units 
whereby  mental  abilities  can  be  relatively  measured. 

Methods  of  procedure  have  been  evolved  by  Pechner,(9> 
Wundt,<32>  Ebbinghaus,<7>  Muller,<17>  and  others,  but  the  appli- 
cation to  pedagogical  problems  has  been  a  comparatively  recent 
development.  Undoubtedly  the  greatest  stimulus  toward  this 
came  from  Binet  in  France,  whose  work  was  quickly  taken  up 
in  Germany  and  in  this  country.  The  various  modifications  and 
elaborations  of  Binet 's  tests  have  filled  the  field  with  a  rich 
literature. 

The  current  interest  in  mental  tests  is  undoubtedly  largely 
due  to  the  need  felt,  on  the  part  of  teachers  and  supervisors, 
for  an  efficient  instrument  wherewith  correctly  to  diagnose  and 
classify  school  children.  This  attitude  is  wholly  in  keeping  with 
the  recent  trend  of  our  public  school  system  which  is  more  and 
more  readjusting  itself  to  the  problem  of  meeting  the  needs  of 
the  individual  child. 

The  following  investigation  is  the  result  of  an  attempt  by 
the  author  to  find  a  satisfactory  scale  for  mental  measurement 


6  A  Graduated  Scale  for  Determining  Mental  Age 

to  be  used  in  the  public  schools.  In  casting  about  for  standard- 
ized tests  none  was  found  which  combined  the  age  scale  with 
the  essentials  of  diagnosis. 

The  novice  in  the  work  is  at  once  attracted  by  the  Binet- 
Simon  scale,  but  it  is  to  be  doubted  if  the  results  obtained  in  its 
application  can  be  considered  reliable.  A  careful  analysis  of 
the  scale,  from  the  standpoint  of  the  psycho-clinicist,  reveals 
many  defects  which  cannot  be  explained  away.  The  scale  falls 
far  short  of  being  the  magical  instrument  which  its  many  ex- 
ponents claim  it  to  be  and  will  never  serve  as  an  instrument  of 
exact  analysis.  However,  a  criticism  of  the  Binet  scale  is  beyond 
the  scope  of  the  present  work,  especially  in  the  light  of  the 
literature  of  the  subject.*  Its  relative  success  in  clinical  work 
would  seem  to  result  from  the  fact  that,  throughout  the  scale, 
there  exists  a  psychological  framework  which  insures  approxi- 
mate results  despite  a  large  amount  of  extraneous  material. 

The  greatest  obstacle  encountered  in  the  practical  applica- 
tion of  any  method  is  the  lack  of  coherence  and  system.  In  the 
measuring  of  mental  processes  the  tests  must  necessarily  cover 
a  wide  range  in  order  to  determine  the  true  ability  of  the  subject. 
Tests  which  ascertain  ability  in  one  phase  must  be  supplemented 
by  tests  applicable  to  other  operations  of  the  mind.  Take,  for 
example  the  Ebbinghaus  "  Combinationsmethode, "  familiarly 
known  as  the  completion  method.  (MB).<JMW)  In  this  test  a 
story  is  given  to  the  child  with  syllables  or  entire  words  omitted 
from  the  text.  The  problem  is  for  the  child  to  fill  in  the  blank 
spaces  in  an  intelligent  manner  in  the  least  possible  time.  The 
author  claims  that  this  is  a  "real  test  of  intelligence,  a  simple, 
easily  applied  device  for  testing  those  intellectual  activities  that 
are  fundamentally  important  and  significant  both  in  the  school 
and  in  life. ' '  Actual  application,  however,  shows  that  the  test  is 
not  as  comprehensive  as  the  author  claims,  is  difficult  to  evalu- 
ate,(24)  and  is  dependent  on  school  training.(30>  But,  in  spite  of 
these  objections,  it  may  be  used  as  one  of  a  group  owing  to  its 
close  correlation  with  intelligence. (6>126) 

The  scale  proposed  in  the  present  monograph  is  an  attempt 
to  combine  the  determination  of  mental  age  with  psychological 
diagnosis.  It  is  composed  of  nine  separate  tests,  divided  into 
three  general  group  ,  as  follows: 

A.  Perception,  tests  I.  and  IX. 

B.  Memory. 

(a)  Auditory,  tests  II.  and  III. 

(b)  Visual,  test  IV. 

(c)  Logical,  test  V. 

C.  Judgment. 

(a)  Visual  proportion,  test  VI. 

(b)  Constructive  problems,  test  VII. 

(c)  Definitions,  test  VIII. 

The  characteristic  features  of  the  scale  are  as  follows:  (1) 
The  same  tests  are  used  for  all  ages  and  the  mental  age  deter- 
mined by  the  manner  of  the  individual  reaction,  measured  in 

*For  criticisms  of  the  Binet  scale  see  especially  references  7,  22, 
23,  24,  27  and  35. 


A  Graduated  Scale  for  Determining  Mental  Age  7 

terms  of  the  relative  number  of  points  for  each  age.  (Norms  have 
been  established  for  the  ages  six  to  fourteen,  inclusive.)  This 
method  dispenses  with  a  great  amount  of  unnecessary  labor, 
both  on  the  part  of  the  experimenter  and  of  the  child,  because 
of  the  fact  that  standing  is  measured  in  terms  of  ability  to 
react.  (2)  The  tests  chosen  are  necessarily  of  such  a  nature 
as  to  appeal  to  the  interest  of  the  child  regardless  of  age.  More- 
over, as  a  proof  that  they  are  genetic  tests  of  intelligence,  the 
ability  to  react  to  each  test  increases  uniformly  as  we  go  up 
the  age  scale,  with  a  fairly  wide  range  between  the  upper  and 
lower  limits.  (3)  The  tests  measure  native  ability  regardless 
of  training.  This  feature  opens  up  a  wide  field  for  discussion. 
For  example,  Binet  uses  as  tests,  counting,  knowledge  of  money, 
family  name,  dates,  and  others  which  may  be  influenced  by 
training.  One  of  my  tests  is  for  the  child  to  name  all  the  objects 
that  he  can  think  of  during  one  minute,  with  the  eyes  closed. 
This  may  be  open  to  criticism  of  training,  but  the  evidence  shows 
that  the  more  intelligent  the  child,  the  greater  the  number  of 
associations,  even  though  the  type  of  words  suggest  the  influ- 
ence of  previous  training  or  environment.  (4)  The  tests  are 
comprehensive,  that  is,  they  are  so  arranged  that  the  several 
basic  mental  operations  may  be  analyzed.  (5)  They  are  compact 
and  systematic.  The  apparatus,  aside  from  the  stop-watch,  can 
be  made  in  the  school  room  or  office,  and,  with  the  exception  of 
the  card  of  objects,  may  be  carried  in  a  large  envelope.  The 
number  of  tests  is  small  but  each  is  important.  (6)  The  tests 
may  be  easily  and  quickly  applied.  It  is  believed  that  any 
teacher  who  understands  the  principles  of  psychological  method 
can,  after  perhaps  fifty  trials,  conduct  the  test  in  about  thirty 
minutes,  with  comparatively  accurate  results.  (7)  The  results 
may  be  accurately  evaluated,  provided  the  data  are  correct. 
This  is  made  possible  by  the  systematic  scoring  by  means  of 
points.*  (8)  The  results  are  significant  from  the  standpoint  of 
the  clinical  psychologist,  indicating  to  the  trained  observer  the 
type  of  the  subject. 

It  is  believed  that  the  scale  is  a  simple  and  coherent  system 
which  may  be  efficiently  used,  both  to  determine  mental  age  and 
mental  type.  In  the  hands  of  the  novice  it  will  indicate  not  only 
the  group  to  which  the  child  belongs,  but  also  his  predominating 
characteristics.  The  expert  will  find  it  valuable  as  an  index  to 
further  tests  which  may  be  deemed  necessary  for  a  more  com- 
plete analysis  of  the  subject's  mentality.  In  any  case,  with 
careful  manipulation,  the  mental  age  will  be  closely  determined. 

Source  of  the  Data. 

In  establishing  the  norms  presented  in  this  work  the  tests 
were  given  personally  by  the  author  to  about  550  children  of 
the  Lincoln  Public  Schools.  Of  this  number,  75  were  tested  be- 
fore the  method  was  fully  worked  out,  about  75  more  were  tested 

*The  entire  plan  of  the  work  was  completed  and  the  data  more 
than  half  collected  before  the  method  of  the  point  scale  used  by 
Yerkes  and  Bridges  (34)  was  available.  Reference  to  their  scale  will 
show  the  radically  different  methods  between  the  two  systems. 


8  A  Graduated  Scale  for  Determining  Mental  Age 

during  the  year  for  clinical  purposes,  leaving  404  in  the  group 
from  which  the  scale  was  ultimately  established,  or  an  average 
of  45  for  each  of  the  nine  ages.  These  children  were  taken  from 
eight  different  schools,  collectively  representative  of  all  classes 
of  population  usually  found  in  a  cosmopolitan  city.  McKinley 
School  is  located  in  the  heart  of  the  business  section  with  a  de- 
cidedly cosmopolitan  community  furnishing  the  students,  with 
a  predominance  of  foreign  shopkeepers  and  peddlers.  Saratoga 
School,  in  the  south  part  of  the  city,  has  grown  up  within  five 
years  to  accommodate  the  children  of  a  multitude  of  small  home 
owners.  Everett  School  is  one  of  the  oldest  in  the  system,  with 
a  very  stable  student  population,  in  a  fairly  well-to-do  commun- 
ity. Whittier  School  is  located  on  the  north  side  in  a  much 
poorer  section  of  the  city  than  those  previously  mentioned,  with 
a  large  German  element  and  many  mechanics.  Bancroft  has  the 
same  class  of  children  in  attendance  as  Whittier.  In  both  of  these 
schools  the  absence  of  fourteen-year-olds  in  the  upper  grades 
was  noticeable.  Capitol  School  is  located  in  the  oldest  residence 
section  with  many  children  of  comparatively  rich  parents  in  at- 
tendance. Clinton  School  is  an  opposite  extreme,  being  located 
in  an  outlying  district  of  cheaper  homes  and  rented  houses.  The 
last  school  visited,  Elliott,  is  located  in  an  average  residence  sec- 
tion and  has  a  stable  attendance. 

The  children  were  selected  by  the  principal  in  conjunction 
with  the  teacher,  after  the  problem  had  been  carefully  explained 
by  the  experimenter.  Teachers  and  principals,  as  well  as  the 
children,  were  intensely  interested  in  the  work  and  put  forth 
every  effort  to  contribute  to  its  success.  It  was  required  of  each 
child  that  he  be  "just  average  or  normal,"  neither  accelerated 
nor  retarded,  that  is,  that  the  pedagogical  age  should  corrsepond 
with  the  chronological  age.  The  child's  physical  development 
and  condition  at  the  time  of  taking  the  test  were  carefully  con- 
sidered. A  great  deal  of  confidence  is  placed  in  the  type  of 
children  selected  because  of  the  fact  that  each  principal  has 
known  practically  each  child  from  the  time  of  entrance,  in  most 
cases  being  entirely  familiar  with  the  child's  family  history. 
Furthermore  the  work  was  undertaken  at  an  opportune  time, 
because  of  the  fact  that  the  Principals'  Club  was  working  on 
the  problem  of  classification,  and  the  principals  were  particular- 
ly interested  in  the  method  of  procedure. 

The  collection  of  data  was  begun  in  November,  1914,  and 
was  continued  until  the  middle  of  June,  1915. 

The  children  of  each  age  group  were  within  the  limits  of 
five  months  over  and  four  months  under  the  year;  for  example, 
the  seven  year  group  ranged  from  six  years  and  eight  months 
to  seven  years  and  five  months,  with  an  average  fairly  close  to 
the  year.  An  effort  was  made  to  keep  the  mean  variation  of  age 
as  low  as  possible. 


A  Graduated  Scale  for  Determining  Mental  Age  9 

TABLE  I. 

Age                      Average  Age  Mean  Variation 

Yrs.    Mo.     Da.  Mo.    Da. 

6   6          1—6  2  —  15 

7  7          0  —  20  2—3 

8   8          0  —  16  2—3 

9  9           o  —     2  2  —  11 

10  10  0  —  15  2—3 

11   11  0—7  2  —  13 

12  12  0—5  2  —  16 

13  13  0  —  19  2  —  12 

14   14  0  —  19  2—6 

Method  of  Conducting  Tests. 

The  method  employed  in  conducting  the  tests  is  similar  to 
that  used  in  the  Binet  tests  and  their  modifications.  A  room  was 
provided  in  each  building  which  would  be  as  quiet  and  free  from 
disturbance  as  possible.  In  a  few  cases  where  it  was  necessary 
to  use  the  principal's  office  the  tests  were  suspended  during  the 
transaction  of  routine  business.  In  each  school  the  experimenter 
was  given  every  possible  consideration  which  contributed  not  a 
little  toward  the  successful  manipulation  of  the  tests.  A  small 
table  was  placed  opposite  the  windows  with  the  experimenter 
seated  facing  the  light  and  with  the  child  on  his  right.  From 
the  moment  the  child  entered  the  room  he  was  treated  with 
cordial  respect  and  made  to  feel  perfectly  at  ease,  with  the  un- 
derstanding that  he  was  contributing  toward  the  solution  of  the 
problem  rather  than  merely  being  tested.  In  some  cases  the 
problem  was  explained  in  some  detail,  while  in  others  the  child 
was  merely  informed  that  his  help  was  desired  in  finding  out 
the  difference  between  the  upper  and  lower  grades.  In  no  case 
was  the  test  begun  until  the  child  felt  at  home  and  was  in  the 
attitude  which  would  produce  uniform  results.  In  the  great  ma- 
jority of  cases  the  children  entered  the  room  with  an  evident  feel- 
ing of  pleasant  anticipation  and  curiosity  due,  perhaps,  to  the 
advertising  which  the  tests  had  received  at  the  hands  of  those 
previously  taking  them.  Each  child  was  cautioned  not  to  tell 
anything  about  the  tests  and  no  evidence  was  discovered  which 
would  indicate  that  they  had  been  talked  over  among  the  chil- 
dren. As  a  matter  of  fact  the  nature  of  the  tests  is  such  that 
previous  information  or  coaching  would  have  but  little  effect  on 
the  final  results.  The  tests  were  all  given  during  the  regular 
school  hours  and  averaged  thirty  minutes  for  each  child.  All 
data  was  recorded  on  the  accompanying  blank.  Drawings  made 
by  the  child  were  kept  on  a  separate  sheet  of  blank  paper 
which  was  later  attached  to  the  blank.  The  recording  was 
done  by  the  experimenter  and  no  effort  was  made  to  conceal  this 
fact  from  the  subject. 


10         A  Graduated  Scale  for  Determining  Mental  Age 

TEST  BLANK 

Name    School Date 

Grade Born „ 

Mental  Age  Age 

I.  Card  of  objects  (5  seconds)  Bu.  Co.  Cr.  Gla.  Ky.  Kni.  Mbl.  Na. 

Ni.  Pn.  Pel.  Pi.  Sci.  Scr.  St. 

II.  Repeating   digits    

III.  Repeating  syllables  

IV.  Learning  figures,  1 2 3 Total 

V.  Association  words  (One  Minute). 

VI.  Height  of  man  standing  by  50-foot  tree.  (Over) feet. 

VII.  Problems  (1)   Square (2)  Rhombus........  (3)  Rectangle 

(4)  Paper  cut (5)  Clock,  9:00 2:00 (6)  Reconstruct 

triangles (7)  Paper  cut 

VIII.  Definitions. 

(1)  Fork. 

(2)  Horse. 

(3)  Automobile. 

(4)  Poet. 

(5)  Tree. 

(6)  Kindness. 

(7)  Sweetness. 

(8)  Charity. 

(9)  Justice. 

(10)     Worm  and  snake. 

IX.  Sorting  cards min sec piles , 

Equivalent  value min sec. 


Test  I. 

In  this  test  fifteen  objects,  familiar  to  all  children,  are 
fastened  on  a  white  card  board  37  cm.  square,  and  covered  with 
another  card  board  of  the  same  dimensions  (See  Fig.  1.)  The 
objects  are  in  description  and  size  as  follows :  One  black  button 
29mm.  in  diameter;  an  aluminum  comb  130mm.  long;  a  green 
crayon  of  standard  form  and  size ;  a  pair  of  blue  glasses ;  a  flat 
Yale  key;  a  pearl-handled  penknife  60mm.  long;  a  blue 
marble  14mm.  in  diameter;  an  eight-penny  nail;  a  Buffalo 
nickel;  a  gold  pen  point;  a  red  paper  pencil  80mm.  long;  a 
red  clay  soap-bubble  pipe ;  a  small  pair  of  scissors ;  an  ordinary 
screw  60mm.  long;  and  a  five-cent  postage  stamp. 

In  giving  the  test  the  covered  card  is  placed  in  front  of 
the  child  and  used  as  a  stimulus  for  close  attention  with  the  ex- 
planation: "I  have  a  lot  of  things  fastened  on  this  card;  now 
I'm  going  to  show  them  to  you  for  just  a  few  seconds  and  then 
when  I  cover  them  up  you  tell  me  what  you  saw.  Now,  look 
closely,  ready — ."  The  objects  are  exposed  for  five  seconds  and 
must  be  covered  quickly  but  quietly.  Any  undue  disturbance 
on  the  part  of  the  observer  is  sufficient  in  some  cases  to  inter- 
fere materially  with  the  reaction.  Incidentally,  it  is  necessary 
to  keep  the  child's  interest  and  attention  focussed  on  the  work 
from  beginning  to  end  of  the  series.  This  is  usually  accom- 
plished by  presenting  the  tests  in  succession  without  pause. 

The  results  are  summarized  in  table  II. 


A  (Jraduated  Scale  for  Determining  Mental  Age 


11 


TABLE    II. 


BOYS 

Age 

No. 

Total 

Av. 

M.  V. 

No. 

Total 

6 

20 

67 

3.3 

.65 

20 

65 

7 

23 

97 

4.2 

.63 

17 

71 

8 

19 

82 

4.3 

.83 

22 

96 

9 

27 

135 

5.0 

.89 

26 

123 

10 

20 

100 

5.0 

.90 

22 

111 

11 

24 

138 

5.8 

.90 

25 

141 

12 

22 

123 

5.6 

1.11 

18 

106 

13 

25 

146 

5.9 

.99 

21 

133 

14 

25 

153 

6.1 

1.12 

28 

184 

GIRLS 


,s 

Av. 

3.3 
4.2 
4.4 
4.7 
5.0 
5.6 
5.9 
6.3 
0.6 

M.  V. 

.57 
.80 
.85 
.85 
1.05 
1.10 
.70 
.85 
1.26 

No. 

40 
40 
11 
53 
42 
49 
40 
46 
53 

BOTH 
Total 
132 
168 

178 
258 
211 
279 
229 
279 
337 

Av.      M.  V 


3.3 
4.2 
4.3 

4.9 
5.0 
5.7 
5.7 
6.1 
6.4 


.61 
.70 
.84 
.85 
.98 

1.01 
.96 
.92 

1.21 


The  increase  of  the  average  number  of  objects  remembered 
for  each  age  is  gixen  in  Figure  2,  which  also  represents  the 
mean  variation  of  the  children  of  each  age  from  their  own 
average,  in  the  lower  graph.  The  curve  shows  that  the  varia- 
bility of  children  in  handling  this  test  increases  materially 
from  six  to  fourteen  years. 

Table  III.  is  a  comparison  of  fourteen-year-old  children 
and  six-year-old  children  in  ability  to  remember  objects. 


A  Graduated  Scale  for  Determining  Mental  A^-e 


* 


u 


7       <5       9       >o      n       n      /s      '">• 


Boys 
Girls 
Both 


TABLE    III. 

6  Yrs. 


3.3 
3.3 


14  Yrs.  %  Increase. 

6.1  sr> 

6.6  100 

6.4  94 


Tables  IV.  and  V.  are  added  to  show  the  interesting;  feature 
of  variability  of  number  of  objects  remembered,  by  boys  (TVJ 
and  «'irls  (V.) 


TABLE    IV. 


Boys. 


A*,-  \,,. 

B.I. 

r.,,. 

Cr. 

Gl. 

Ky. 

Kni 

.  Ml,. 

\:i. 

Ni. 

I'n. 

Pel. 

Pi. 

Sri. 

Br. 

s«. 

li  20 

1 

5 

5 

s 

4 

7 

5 

1 

1 

I) 

3 

13 

10 

2 

1 

7  23 

1 

11 

7 

13 

9 

12 

8 

1 

1 

2 

12 

14 

5 

0 

1 

8  19 

1 

Y 

5 

!; 

8 

10 

5 

O 

0 

1 

7 

10 

T 

4 

2 

9  27 

2 

1'! 

9 

20 

11 

14 

9 

5 

8 

5 

7 

13 

11 

3 

6 

10  20 

1 

11 

12 

14 

6 

10 

6 

1 

9 

4 

8 

6 

9 

1 

2 

11  24 

2 

12 

13 

17 

9 

15 

10 

6 

10 

2 

10 

13 

10 

5 

4 

12  22 

3 

9 

9 

13 

9 

12 

5 

2 

11 

4 

11 

11 

11 

3 

10 

13  25 

3 

15 

9 

16 

10 

13 

9 

9 

14 

4 

10 

17 

7 

5 

5 

14  25 

3 

15 

12 

17 

8 

15 

6 

6 

14 

8 

11 

12 

11 

6 

9 

Total 

17 

9G 

81 

126 

74 

108 

63 

34 

71 

30 

79 

109 

80 

29 

40 

TABLE 

V. 

Girls 

A?,-  No. 

Bu. 

Co. 

Cr. 

Gl. 

Kv. 

Km. 

Ml,. 

Yi. 

Ni. 

PH. 

P.-I. 

Pi. 

Sri. 

Sr. 

St. 

6  20 

1 

3 

2 

14 

3 

5 

8 

3 

2 

0 

9 

12 

3 

o 

1 

7  17 

1 

- 

9 

10 

4 

5 

7 

2 

4 

0 

5 

6 

10 

0 

1 

8  22 

4 

11 

g 

IS 

2 

4 

4 

0 

7 

3 

10 

9 

11 

3 

1 

9  26 

2 

12 

8 

18 

g 

10 

11 

3 

10 

3 

11 

16 

12 

2 

2 

10  22 

2 

6 

13 

18 

5 

12 

5 

6 

4 

5 

12 

11 

14 

3 

5 

11  25 

4 

11 

18 

20 

5 

13 

7 

1 

9 

6 

10 

10 

16 

4 

7 

12  18 

4 

9 

9 

14 

7 

6 

5 

3 

6 

5 

10 

9 

14 

2 

0 

13  21 

6 

11 

13 

11 

8 

5 

11 

3 

1.1 

4 

12 

14 

17 

1 

6 

14  28 

(5 

19 

16 

21 

10 

14 

9 

5 

12 

- 

15 

17 

13 

6 

14 

Total      :!()     89     97     144     4<;     74     67     20     05     33     94     104     110     21     40 


A  Graduated  Scale  for  Determining  Mental  Age          13 

A  comparison  of  the  totals  of  the  above  tables  indicates 
the  following  sex  differences:  The  girls  mention  the  button, 
crayon,  glasses,  pencil  and  scissors,  a  significant  number  of  times 
more  than  do  the  boys;  the  boys  mention  the  key,  knife,  nail, 
nickel,  and  screw  oftener  than  the  girls;  they  rank  about  the 
same  in  the  case  of  the  comb,  marble,  pen,  pipe  and  stamp.  This 
comparison,  while  somewhat  irrelevant,  is  significant  to  the 
psychologist,  and  is  represented  graphically  in  figure  3. 


Bu,  Ca  Cr  Crt.    Ky.  Kni  Mb.  Na.  A// .  Prt.  ft/.  Pi.  Sc/.  6  r  6/r 


70 


Figr.  3. 


TestH. 

The  second  test  is  one  used  by  Binet  and  universally 
adopted  by  those  who  have  made  modifications  of  the  Binet- 
Simon  scale,  namely,  auditory  memory  for  digits.  For  conveni- 
ence the  child  is  requested  to  look  at  a  designated  object  which 
will  turn  him  sidewise,  with  the  right  side  to  the  experimenter. 
This  method  was  found  more  convenient  than  to  have  the  child 
turn  completely  around  and  moreover  gives  the  experimenter 
an  opportunity  to  discover  whether  the  subject  is  of  the  motor 
type  by  watching  the  movement  of  the  lips  while  giving  the 
syllables.  The  only  explanation  given  is  "Say  these  numbers 
after  me."  The  following  digits  are  then  read  in  a  smooth,  even, 
distinct  voice,  without  accent  except  for  a  natural  lowering  of 
the  voice  on  the  last  digit  of  each  group,  which  becomes  the 
signal  for  the  child  to  begin  repeating.  The  rate  is  slightly  faster 
than  one  digit  per  second. 


14         A  Graduated  Scale  for  Determining  Mental  Age 

29  847         4297         52814         384296         1695847         41629385 

315        5318        47395        279314         2964375        25718394 

73  926         6194         58319         618492         9285164        58261947 

The  child  is  required  to  repeat  correctly  two  out  of  any 
given  group  in  order  to  receive  credit  for  that  group.  In  other 
words,  he  is  given  credit  for  the  number  of  digits  in  the 
highest  group  in  which  he  is  able  to  repeat  correctly  two  num- 
bers. For  example,  in  the  fours  he  may  repeat  4-2-9-7  correctly, 
fail  in  repeating  5-3-1-8,  and  then  repeat  6-1-9-4  correctly, 
when  he  will  proceed  to  the  next  higher  group.  Then  in  the 
fives,  if  he  should  make  one  correct  repetition,  but  fail  in  the 
other  two,  his  credit  is  for  four  digits  only. 

Table  VI.  contains  the  results  of  this  test  with  the  number 
of  digits  repeated  correctly  and  the  mean  variation  for  each 
age. 


BOYS 


Age  No.  Total 

6  20  87 

7  23  116 

8  19  102 

9  27  154 

10  20  113 

11  24  139 

12  22  133 

13  25  154 

14  25  160 


TABLE  VI. 
Repeating  Digits. 


GIRLS 


AT. 

M.V. 

No. 

Total 

4.3 

.54 

20 

90 

5.0 

.52 

17 

82 

5.4 

.81 

22 

124 

5.7 

.58 

26 

146 

5.7 

.47 

22 

121 

5.8 

.53 

25 

146 

6.0 

.50 

18 

106 

6.1 

.44 

21 

127 

6.4 

.74 

28 

177 

Av. 

4.5 
4.9 
5.6 
5.6 
5.5 
5.8 
6.0 
6.0 
6.3 


BOTH 


M.V.  No.  Total 

.70  40  177 

.60  40  198 

.78  53  226 

.81  53  300 

.73  42  234 

.61  49  285 

.33  40  239 

.43  46  281 

.68  53  337 


AT.       M.  V. 

4.4  .64 
4.9  .56 
.80 
.70 
.62 
.57 
.43 
.44 
.70 


5.5 
5.7 
5.6 
5.8 
6.0 
6.1 
6.4 


7 


3      /O     II 

Fig,   4. 


12. 


A* 


It  will  be  noticed  here  that  the  increase  is  greatest  from 
six  to  eight,  with  a  slight  drop  at  ten,  and  a  constant  increase 
from  ten  to  fourteen.  The  per  cent,  of  increase  in  Mo  from 
six  to  fourteen  is  given  in  table  VII.  The  increase  in  ability  to 
repeat  digits  is  shown  graphically  in  figure  4,  the  lower  curve 
showing  the  variability  of  the  mean  variation,  which  is  greatest 
at  eight  and  lowest  at  twelve  and  thirteen. 


A  Graduated  Scale  for  Determining  Mental  Age         15 


TABLE  VI 

1. 

6Yrs. 

14  Yrs. 

%  Increase. 

Boys    

4.3 

6.4 

49 

Girls         

4.5 

6.3 

40 

Both 

4.4 

6.4 

46 

Test  in. 

The  third  test  is  also  taken  from  Binet  and,  like  the  pre- 
ceding one,  is  a  test  of  auditory  memory.  It  consists  in  re- 
peating syllables  in  sentence  form,  beginning  with  a  word  of 
two  syllables,  with  each  succeeding  sentence  or  group  of  words 
greater  than  the  preceding  by  two  syllables.  The  sentences  used 
are  Goddard's  modification  of  those  given  by  Binet  and  Simon 
and  are  taken  from  Whipple's  Manual.(28) 

1.  Papa. 

2.  Slipper.  Letter. 

3.  It  is  cold  and  snowing. 

4.  I  have  a  dog.   He's  a  fine  one. 

5.  His  name  is  Jack.  Oh,  what  a  naughty  boy. 

6.  It  is  raining  out  doors,  but  we  can  stay  inside. 

7.  We  are  having  a  fine  time.   We  found  a  mouse  in  a 
trap. 

8.  Let's  all  go  for  a  walk  today.    Give  me  that  big  hat 
to  wear. 

9.  Poor  Helen  has  just  torn  her  new  dress.     She   will 
surely  feel  sorry  for  that. 

10.  Why  should  anyone  want  to  do  injury  to  such  beau- 
tiful creatures  as  birds? 

11.  We  expect  to  have  a  great  time  at  the  seashore,  digging 
in  the  white  beach  sand  all  day  long. 

12.  When  the  train  crosses  the  road  the  engineer  will  see 
the  wagon  standing  beside  the  apple  tree. 

13.  My  young  brother  Frank  had  a  fine  time  on  his  vaca- 
tion this  summer.   He  went  fishing  almost  every  day. 

14.  To  start  a  fire  in  the  open  is  one  of  those  tricks  which 
everyone  thinks  he  can  perform  until  he  tries  it. 

15.  He  sinks  the  net  in  the  water  and  waits  until  he  can 
see  the  fish  distinctly,  lying  perfectly  still  and  within 
reach. 

16.  The  first  rapid  was  only  the  beginning;  half  a  mile 
below  we  could  see  the  river  disappear  between  two 
points  of  rock. 

17.  One  day  the  children's  grandmother    came    to    visit 
them  and  the  children  were  very  happy  because  she 
told  them  beautiful  fairy  stories. 

18.  The  Indians  used  to  perform  many  kinds  of  queer, 
horrible  dances,  in  the  course  of  which  they  yelled  and 
shrieked  as  if  suffering  the  most  painful  torture. 

It  is  necessary  to  pronounce  the  words  distinctly,  at  a 
uniform  rate,  and  without  undue  accent.  The  main  objection  to 
this  test  is  the  lack  of  uniform  increase  in  difficulty  from  one 
sentence  to  the  next.  For  example,  I  found,  as  did  Mrs.  Squire(22) 
and  others,  that  the  children  could  often  repeat  the  twelfth 


16         A  Graduated  Scale  for  Determining  Mental  Age 

sentence  correctly  after  having  failed  in  the  two  or  three  pre- 
ceding sentences.  Hence,  after  my  preliminary  tests,  I  changed 
the  sentence  from  "When  the  train  crosses  the  road  the  engineer 
will  Now  the  whistle  and  the  fireman  will  ring  the  bell,"  to 
"When  the  train  crosses  the  road  the  engineer  will  see  the  wagon 
standing  beside  the  apple  tree,"  a  sentence  less  rich  in  associa- 
tive connections. 

This  test  is  given  under  the  same  conditions  as  the  second 
and  should  follow  it  without  a  break  with  the  simple  state- 
ment, "Repeat  these  words."  It  will  be  noticed  that  the  general 
method  of  procedure  in  this  and  the  preceding  test  differs  from 
that  given  by  Binet  in  that  the  child's  maximum  ability  is 
found  at  once,  that  is,  without  interposing  other  tests  and  then 
reverting  to  the  memory  tests,  if  ability  of  a  higher  age  is  shown. 

In  order  to  receive  credit  for  a  sentence  it  is  considered 
necessary  for  the  child  to  repeat  every  syllable  correctly.  But  if 
a  slight  error  occurs  in  one  sentence,  and  the  child  can  repeat  the 
next  correctly,  he  is  given  credit  for  the  latter.  I  made  one  con- 
cession in  regard  to  verbatim  repetition  in  the  eleventh  sentence. 
Here  I  accepted  as  correct  "fine  time  at  the  seashore,"  whereas 
the  sentence  reads  "great  time  at  the  seashore."  This  mistake 
occurred  so  frequently  in  the  preliminaries  in  the  cases  of  chil- 
dren who  could  repeat  the  two  succeeding  sentences  that  I  felt 
justified  in  making  the  change. 

In  no  case  is  the  child  informed  of  his  errors;  when  the 
maximum  has  been  reached  we  pass  immediately  to  the  next  test 
as  if  there  were  no  more  sentences  to  be  given.  In  this,  as  in 
all  the  other  tests,  the  average  child  will  watch  for  confirma- 
tion of  his  work.  It  is,  of  course,  necessary  for  the  experimenter 
to  be  perfectly  passive,  and  give  no  sign  of  commendation  prior 
to  the  completion  of  the  work  in  hand. 

At  an  early  stage  in  the  work  I  discovered  that  considera- 
ble time  could  be  saved  by  beginning  with  the  fourth  sentence 
for  the  lower  ages  and  with  the  seventh  or  eighth  for  the  upper 
ages. 

TABLE  VIII. 
Summary  of  Test  III,    Ability  to  Repeat  Syllables. 

BOYS  GIRLS  BOTH 

Age     No,     Total          Av.         M.  V.     No.      Total  Av*       M.  V-      No.       Total  Av.       M.  V. 

6  20  310  15.5  1.4  20  318  15.9  .77  40  628  15.7  1.08 

7  23  374  16.3  1.1  17  268  15.8  1.08  40  642  16.0  1.09 

8  19  322  16.9  1.5  22  378  17.2  1.55  41  700  17.1  1.53 

9  27  492  18.2  1.75  26  470  18.0  1.46  53  962  18.1  1.60 

10  20  354  17.7  1.73  22  404  18.4  1.75  42  758  18.0  1.74 

11  24  492  20.5  2.25  25  471  18.8  1.76  49  963  19.7  2.00 

12  22  448  20.4  2.19  18  363  20.2  2.10  40  811  20.3  2.15 

13  25  582  23.4  2.97  21  448  21.3  2.14  46  1030  22.4  2.60 

14  25  610  24.4  2.91  28  662  23.6  3.05  53  1272  24.0  2.99 

The  increase  in  ability  to  repeat  syllables,  according  to  this 
data,  is  fairly  uniform,  with  a  close  parallelism  between  the  two 
sexes.  The  greatest  increase  is  between  the  ages  of  twelve  and 
thirteen,  with  a  slight  drop  between  nine  and  ten.  My  results 
agree  with  those  of  Binet  showing  twenty-four  syllables  for 


A  Graduated  Scale  for  Determining  Mental  Age         17 

the  fourteen  year  group  while  the  Binet  tests  use  twenty-six  for 
the  fifteen  year  group. 


9       10      II      12 

Fig.   5. 


The  comparative  ability  of  the  fourteen  and  six  year  group 
is  given  in  table  IX. 


Boys   

Girls    

Both  .. 


TABLE  IX. 

6  Yrs.  14  Yrs. 

..     15.5  24.4 

15.9  23.6 

15.7  24.0 


%  Increase. 
57 
48 
53 


Curves  for  variation  in  ability  to  repeat  syllables,  and  mean 
variation  for  the  different  ages  are  given  in  figures  5. 


*  18         A  Graduated  Scale  for  Determining  Mental  Age 

Test  IV. 

Immediately  following  the  third  test  the 

T  child  is  given  a  test  involving  visual  and  motor 
memory.  The  material  used  is  five  odd  shaped 
figures  which  have  been  adopted  from  those  given 
in  Seashore's  Manual.  <19«132>  By  referring  to 
figure  6  it  will  be  noticed  that  these  are  made 
up  of  a  vertical  and  a  horizontal  line,  each  thir- 
___  teen  mm.  in  length,  and  drawn  at  right  angles  to 
one  another.  At  the  opposite,  or  unattached  end 
of  the  vertical  line,  a  third  line,  six  and  one-half 
VI  mm.  in  length,  is  drawn,  at  an  angle  of  45°.  The 

^1  variation  in  form  of  the  figures  is  made  by  differ- 

ent combinations  of  these  three  lines.   The  first 
m mmmmm^       and  last,  the  second  and  fourth,  may  be  said  to 
be  pairs,  in  that  they  are  identical  but  inverted. 
This  similarity  was  noticed  by  some  children  and 
^1       became  an  aid  in  memorizing  the  figures. 
^|  The  method  is  as  follows :  The  child  is  given 

a  piece  of  blank  paper  and  shown  the  figures  for 
perhaps  a  second  while  the  operator  makes  this 
explanation:  "Now  I'm  going  to  let  you  look  at 
these  things  for  just  a  few  seconds,  and  then 
^H  when  I  take  them  away,  you  draw  as  many  as 

you  can  remember.  Here's  the  pencil."  The  fig- 
ures are  removed  at  the  word  "seconds."   This 
I— •»       places  the  child  in  the  proper  attitude  and  shows 
definitely  what  is  wanted  in  the  briefest  possible 
amount  of  time.    I  hit  upon  this  method  after 
several  experiments  in  the  preliminaries,  during 
^^         which  I  used  the  word  "figures."  I  found  that 
this  suggested  the  arabic  figures,  hence  I  adopted 
the  word  "things"  while  letting  the  child  see  the 
(••JL-M*       objects  themselves.  Following  the  above  explana- 
F1     6  tion,  after  a  pause  of  about  two  seconds  to  notice 

by  the  child's  expression  whether  or  not  the 
problem  was  clear,  the  slip  on  which  the  figures  were  drawn  is 
placed  on  the  blank  paper  directly  in  front  of  the  child  with 
the  remark:  "Now  study  them  carefully."  After  an  exposure 
of  ten  seconds  the  slip  is  quietly  but  quickly  removed  and  the 
child  told  to  draw  as  many  as  he  can  remember.  During  this 
process  the  operator  must  be  absolutely  quiet.  A  slight  dis- 
turbance may  interfere  with  the  reaction,  but  in  general,  the 
child  draws  at  once  all  of  the  figures  which  he  remembers.  I 
found  that  it  was  useless  to  wait  for  further  results  after  about 
fifty  seconds.  When  the  child  has  drawn  as  many  figures  as 
possible  from  the  first  exposure  his  paper  is  turned  over  or 
covered  up  for  another  trial,  with  the  remark  "Draw  here  next 
time,"  which  indicates  that  the  experiment  is  to  be  repeated, 
and  also  inhibits  the  tendency  to  look  at  the  previous  work. 
The  test  is  given  three  times  with  the  same  instructions  in  each 
instance.  The  child  is  not  permitted  to  look  at  his  work  until 


A  Graduated  Scale  for  Determining  Mental  Age         19 

the  three  trials  are  finished  and  no  hint  should  be  given  con- 
cerning his  accuracy  until  the  completion  of  the  test. 

In  evaluating  this  test  I  allow  one  point  for  each  figure 
correctly  drawn,  giving  full  credit  for  repetition  of  figures 
drawn  in  succeeding  trials,  but  not  for  figures  duplicated  in  the 
same  trial.  Half  credit  is  given  if  a  figure  is  reversed,  but  no 
credit  if  a  figure  is  inverted. 

After  a  little  practice  the  operator  is  able  to  count  the 
number  of  correct  figures  while  the  child  is  drawing  them,  im- 
mediately filling  in  the  blank.  The  data  for  each  trial  were 
kept  separate,  but  in  the  following  table,  which  gives  the  sum- 
mary, the  total  for  the  three  trials  is  used. 

TABLE  X. 

Summary  of  Test  IV.,  Visuo-motor  Memory. 

BOYS  GIRLS  BOTH 

Age     No.       Total  AT.       M.  V.      No.       Total  Av.       M.  V.     No.        Total  AT.     M.  V. 

6     20      41.0      2.0     1.3       20      31.5        1.6       .96     40       72.5        1.8     1.12 


7  23 

64.0 

2.8 

1.43 

17 

38.5 

2.3 

1.19 

40 

192.5 

2.6 

1.28 

8  19 

67.0 

3.5 

1.21 

22 

67.0 

3.1 

1.55 

41 

134.0 

3.3 

1.4 

9  27 

125.5 

4.6 

1.56 

26 

87.5 

3.0 

1.40 

53 

213.0 

4.0 

1.54 

10  20 

86.5 

4.3 

1.54 

22 

100.0 

4.5 

1.82 

42 

185.5 

4.4 

1.69 

11  24 

138.0 

5.7 

2.36 

25 

123.5 

4.9 

1.47 

49 

261.5 

5.3 

1.84 

12  22 

129.0 

5.9 

1.82 

18 

93.5 

5.2 

1.66 

40 

222.5 

5.6 

1.82 

13  25 

171.5 

6.8 

1.83 

21 

142.0 

6.7 

1.71 

46 

313.5 

6.8 

1.80 

14  25 

203.0 

8.1 

1.62 

28 

195.0 

7.0 

1.7 

53 

398.0 

7.5 

1.86 

This  proved  to  be  one  of  the  most  interesting  and  valuable 
of  the  entire  series  of  tests.  The  method  of  drawing  the  figures, 
the  motions  with  the  pencil  which  often  accompany  the  learn- 
ing, and  other  facts  which  arise  in  individual  cases,  make  the 
test  of  especial  use  in  diagnosis,  aside  from  its  value  as  a  unit 
in  the  present  work.  For  example,  a  student  who  is  a  distinct 
motor  type  will  trace  the  figures  in  the  air  while  studying  them. 
Mature  students  who  are  proficient  in  hand  work  will  draw  with 
accuracy  and  precision  regardless  of  their  ability  in  other  lines 
of  work.  Moreover,  the  correlation  with  intelligence*  is  very 
close,  the  curve  being  strikingly  parallel  with  the  summation 
curve  shown  in  figure  18. 

The  norms  show  a  typical  increase  in  ascending  the  age 
scale,  with  a  comparatively  small  mean  variation.  See  figure 
7.  This  test  fully  meets  the  important  requirements  of  an  in- 
telligence test,  being  uniform  throughout,  and  having  a  wide 
range  between  the  upper  and  lower  limits,  as  shown  in  table  XI. 

TABLE  XI. 

6  Yrs.  14  Yrs.  %  Increase. 

Boys    2.0  8.1  300 

Girls    1.6  7.0  338 

Both    1.8  7.5  317 


20 


A  Graduated  Scale  for  Determining  Mental  Age 


6        7      6       9       0      U       12      13     /+ 

Fig-.    7. 

Test  V. 

Number  of  Objects  Named  in  One  Minute. 

This  test  is  adapted  from  the  third  test  in  Binet's  twelve 
year  series,  in  which  the  child  is  required  to  name  as  many 
words  as  he  can  in  three  minutes.  My  instructions  to  the  child 
are  as  follows:  "Shut  your  eyes.  Now  name  over  all  the  things 
you  can  think  of;  just  any  thing — any  object."  This  is  usually 
sufficient  except  in  a  minority  of  cases  in  the  lower  years.  If 
the  child  does  not  understand  he  will  say  so,  perhaps  opening  his 
eyes,  in  asking  for  further  information.  In  such  a  case  it  may  be 
necessary  to  explain  what  is  meant  by  thing;  ordinarily  the 
statement  "A  book  is  a  thing"  is  sufficient  to  start  the  reaction. 
The  child  will  shut  his  eyes  and  begin  with  the  word  book.  I 
snap  the  watch  at  the  sound  of  the  first  word,  allowing  the  re- 
action to  continue  for  one  minute.  If  the  key- word — book — is 
required,  it  is  not  counted  in  the  total  number  of  words.  Credit 
is  given  for  the  common  nouns  only.  If  the  child  gets  started 
on  a  series  of  proper  names  it  is  necessary  to  interrupt  with  the 
expression,  "No,  not  that  kind,  just  common  things."  This 
occurs,  however,  very  seldom.  The  most  interesting  case  of  the 
kind  was  noticed  during  the  preliminary  trials.  A  very  pre- 
cocious girl  of  ten  years  started  to  name  the  states  and  was 
well  down  the  list  before  sidetracked.  Occasionally,  in  the  lower 
ages,  the  child  will  need  additional  stimulus.  During  longer 
pauses  suggestive  of  waning  attention,  I  break  in  with  "Some- 
thing else/'  which  serves  to  renew  the  effort. 

For  purposes  of  diagnosis  the  words  should  be  taken  down, 
but  I  found  it  impracticable  to  do  so  except  for  the  younger 
children.  From  the  psychological  standpoint  this  test  is  inter- 
esting and  very  significant  in  its  bearing  on  mental  ability. 
"Besides  the  number  of  words,  one  can  note  their  relations; 
some  subjects  give  only  detached  words,  each  of  which  requires 
an  effort  to  recall.  Others  give  a  series  of  words,  the 
furnishings  of  a  school,  various  articles  of  clothing,  etc.  Some 


A  Graduated  Scale  for  Determining  Mental  Age         21 

use  only  names  of  common  objects,  others  cite  abstract  qual- 
ities or  rather  far-fetched  words.  All  this  gives  an  idea  of  the 
mentality  of  the  subject.'^4'50)  A  series  given  by  a  child  of  six 
may  contain  words  which  have  no  obvious  relation;  as,  for  ex- 
ample, the  following:  pencil,  garden,  doll,  boat,  horse,  chair. 
On  the  other  hand  a  mature  child  names  objects  in  a  regular 
series  of  associated  words,  often  without  a  break.  The  following 
list  was  given  by  a  boy  of  ten:  book,  school,  tires,  building, 
house,  sideivalk,  street,  ground,  street  car,  trolley,  iron,  black- 
smith shop,  cigars,  candy,  confectionery,  paper,  pencil,  music, 
music  rack,  piano,  flute,  book,  magnifying  glass,  orange,  potato, 
radish,  beet,  carrot,  turnip,  hygiene.  Rapidity  of  naming  ob- 
jects is,  of  course,  facilitated  by  association,  hence  the  older 
child  will  give  a  greater  number  of  words.  "Little  children  ex- 
haust an  idea  in  naming  it;  they  say,  for  example,  hat,  then 
pass  on  to  another  object  without  noticing  that  hats  differ  in 
color,  in  form,  have  various  parts,  have  different  uses  and  acces- 
sories. .  .  .  Their  lack  of  skill  in  the  use  of  language,  and  in 
the  analysis  of  ideas,  is  very  striking.  "(4«53) 

It  is  evident  that  there  is  a  close  correlation  between  general 
intelligence  and  ability  to  enumerate  objects.  It  is  also  evident 
that  this  ability  increases  with  the  growth  of  richness  in  as- 
sociation until  the  age  of  twelve  when  the  maximum  seems  to 
have  been  reached.  Hence,  for  the  present  purpose,  the  results 
are  evaluated  by  merely  counting  the  number  of  things  named 
— the  number  of  common  nouns — leaving  the  analysis  of  the 
train  of  associated  words  for  application  in  diagnosing  the  in- 
dividual case. 

It  is  believed  that  the  method  here  presented  is  superior 
to  that  used  by  Binet,  for  three  reasons:  (1)  By  having  the 
eyes  closed  the  material  is  to  a  great  extent  introspective.  The 
child  may  begin  by  naming  the  objects  which  he  has  just  seen  on 
the  table,  but  quickly  switches  to  the  schoolroom,  the  home,  or 
the  playground.  (2)  By  allowing  one  minute  instead  of  three 
time  is  saved  and  the  child  is  not  fatigued.  The  number  of 
words  in  the  first  twenty  seconds  is  usually  greater  than  that  of 
the  last  forty,  and  no  advantage  can  be  gained  by  prolonging 
the  time.  (3)  The  instructions  are  given  in  a  manner  which 
causes  the  child  to  name  nouns — ideas — rather  than  words. 

In  the  majority  of  cases  I  was  assured  of  a  maximum  of 
effort  on  the  part  of  the  children.  This  can  be  noticed  by  the 
facial  expression,  which  can  be  carefully  studied  while  the  eyes 
are  closed  for  this  exercise. 

TABLE  XII. 
Number  of  things  named  in  one  minute. 

BOYS  GIRLS  BOTH 

Age      No.     Total  Av.         M.  V.      No.     Total  Av.         M.  V.     No.        Total  Av.        M.  V 

6  20  268  13.4  5.3  20  235  11.7  3.95  40  503  12.5  4.65 

7  23  327  14.2  4.2  17  239  14.1  5.02  40  566  14.2  4.57 

8  19  350  18.4  4.6  22  380  17.3  4.82  41  730  17.8  4.69 

9  27  624  23.1  5.36  26  554  21.3  4.70  53  1178  22.2  5.36 

10  20  453  22.6  6.05  22  485  22.0  6.40  42  938  22.3  6.22 

11  24  704  29.3  6.56  25  639  25.6  4.97  49  1343  27.4  5.82 

12  22  661  30.0  4.55  18  628  34.9  6.37  40  1289  32.2  6.45 

13  25  775  31.0  7.28  21  606  29.0  9.19  46  1381  30.0  7.72 

14  25  776  31.0  5.64  28  924  33.0  6.36  53  1700  32.1  5.85 


22         A  Graduated  Scale  for  Determining  Mental  Age 

The  curve  indicating  increase  in  number  of  things  named 
is  given  in  figure  8.  The  increase  is  greatest  between  the  ages 
seven  and  nine,  ten  and  twelve.  No  gain  is  made  from  twelve 
to  fourteen.  The  drop  between  twelve  and  thirteen  is  caused  by 
a  lessened  ability  on  the  part  of  the  girls,  which  can  perhaps 
be  traced  to  physiological  causes.  The  boys  outrank  the  girls 
in  all  ages  except  at  twelve  and  fourteen. 

The  lower  curve  of  figure  8  shows  the  fluctuation  of  the 
mean  variation.  This  curve  is  strikingly  similar  to  the  curve 
of  increase  in  ability  (the  upper),  except  that  the  variations 
are  one  year  later.  For  example,  at  ten  years  the  mean  variation 
is  high,  while  the  increase  in  ability  over  the  preceding  year  is 
but  slight;  at  eleven  the  mean  variation  drops,  while  the  ability 
curve  rises;  at  thirteen  the  mean  variation  is  high,  with  a  cor- 
responding drop  in  ability;  at  fourteen  the  conditions  are  just 
the  reverse. 

The  per  cent,  of  gain  of  the  fourteen  year  old  children  over 
the  six  year  old  children  in  number  of  ideas  named  during  one 
minute  is  given  in  table  XIII. 

TABLE  XIII. 


Boys 
Girls 
Both 

6 
] 

Yrs.             14  Yrs.     %  Increase. 
.3.4                31.0                134 
1.7                33.0                182 
•2.5                32.1                157 

1 

/ 

<, 

7 

[/- 

~^^~ 

tf^ 

'j 

*>l 

****I.P/1 

^' 

I 

\ 

K-    —  * 

| 

V** 

la 

-4 
< 

^ 

^ 

,/, 

N\ 

^ 

^ 

/ 

s<^ 

^/ 

v  1 

V 

rt> 

\ 

'x 

/    \ 

1 

\ 

5 

4 

^ 

\^/ 

~"  •  —  i 

^-J\ 

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b       7       6       * 

)      10       n       12      /S      A 

Fig.   8. 

Test  VI. 

The  sixth  test  is  a  problem  involving  judgment  of  visual 
proportion.  The  child  is  told  to  draw  a  picture  of  a  tree  which 
is  fifty  feet  high,  with  a  man  standing  by  it.  For  ages  six  and 
seven  this  was  varied,  because  of  the  fact  that  the  term  fifty 
feet  possesses  but  little  significance  for  younger  children.  In 
fact,  it  was  doubted  at  first  whether  this  would  be  a  test  ap- 


A  Graduated  Scale  for  Determining  Mental  Age         23 

plicable  to  all  ages,  but  subsequent  trials  proved  it  to  be 
especially  valuable.  The  children  of  six  and  seven  years  of  age 
were  told  to  draw  "A  great,  big,  high  tree,  fifty  feet  high  with 
a  man  standing  by  it."* 

The  height  of  the  tree  and  man  were  measured  in  milli- 
meters and  the  comparative  height  of  the  latter  computed  at 
once  on  the  slide  rule  by  means  of  the  following  simple  formula : 
H=50  M/T,  where  H  represents  the  required  height  of  the  man, 
M  actual  height  of  man  in  millimeters,  and  T  actual  height  of 
tree  in  millimeters.  In  practice  I  measure  M,  divide  by  2, 
mentally,  then  on  the  slide  rule  divide  this  by  T,  properly  plac- 
ing the  decimal. 

While  the  children,  with  a  few  exceptions,  had  taken  the 
regular  course  in  drawing,  the  sense  of  proportion  does  not  dis- 
play itself,  except  relatively,  until  the  later  years  are  reached. 
A  consistent  effort  to  draw  to  scale  is  not  shown  except  during 
the  years  thirteen  and  fourteen,  and  then  only  in  scattered  in- 
stances. In  general,  the  crudest  drawings  are  accompanied  by 
the  poorest  sense  of  proportion.  "We  have  exemplified  here  the 
development  of  the  ability  of  self  expression  through  drawing. 
The  children  of  six  make  the  customary  rectangular  trunk  with 
a  spray  of  branches  protuding  from  the  upper  end.  The  lack 
of  co-ordination  of  the  accessory  muscles  is  shown  by  the  square 
head  and  body  of  the  man.  Training  in  drawing  displays  itself 
in  the  style  of  tree  (for  example,  during  the  holiday  season  the 
children  all  drew  Christmas  trees),  but  there  is  no  evidence  of 
transfer  to  ability  to  judge  proportion. 

The  relative  height  of  the  man  with  variations  is  given  in 
table  XIV. 

TABLE  XIV. 
Man  and  Tree 

BOYS  GIRLS  BOTH 

Age    No.       Total  Av.        M.  V.     No.       Total         Av.        M.  V.      No.      Total         Av.       M.  V. 

6  20  389.0  19.4  5.33  20  443.6  22.1  6.29  40  832.6  20.8  5.86 

7  23  441.3  19.2  5.18  17  415.5  24.4  7.83  40  856.8  20.4  7.30 

8  19  397.0  20.9  6.80  22  255.8  16.2  4.11  41  752.8  18.4  6.00 

9  27  430.8  15.9  4.80  26  535.9  20.6  7.66  53  966.7  18.2  6.83 

10  20  328.5  16.4  6.29  22  453.8  20.6  7.67  42  782.3  18.6  7.32 

11  24  365.7  15.2  5.80  25  346.3  13.7  4.31  49  712.0  14.5  4.70 

12  22  214.4  9.8  3.52  18  304.5  16.9  8.17  40  518.9  12.9  6.56 

13  25  302.3  12.1  4.46  21  293.0  14.0  7.52  46  595.3  12.9  5.90 

14  25  290.5  11.6  3.92  28  331.4  11.8  4.80  53  621.9  11.7  4.36 

The  comparative  height  of  the  man  for  the  different  ages 
is  indicated  in  the  upper  graph  in  figure  9.  The  irregularity 
is  to  be  expected  from  six  to  nine.  The  ten  year  group  shows 
a  weakness  in  the  sense  of  proportion  while  a  marked  gain  is 
shown  from  ten  to  twelve.  There  is  no  improvement  from 
twelve  to  thirteen,  but  a  decided  advance  from  thirteen  to  four- 
teen. The  boys  indicate  a  higher  ability  in  this  problem  than 
the  girls;  furthermore  the  points  of  greatest  increase  for  the 

*A11  drawings  made  by  the  child  are  kept  on  the  sheet  of  blank 
paper  furnished  him  in  test  IV. 


24         A  Graduated  Scale  for  Determining  Mental  Age 


boys  are  coincident  with  a  backward  drop  for  the  girls,  for 
example,  ages  nine,  ten  and  twelve. 


i 

3 


5 


i 


y     to     //      /2     /5     /4 

Fig.    9. 

The  curve  of  mean  variation  and  that  indicating  relative 
height  of  the  man,  are  strikingly  similar.  The  two  curves  for 
girls  are  virtually  parallel.  Likewise  the  curves  for  boys,  and 
the  curves  for  the  entire  group.  This  signifies  that  the  groups 
which  show  greatest  ability  in  judging  the  proportionate  height 
of  the  man  are  the  least  variable. 

While  the  curve  is  more  irregular  than  one  would  hope 
for,  nevertheless  the  test  has  great  value  in  diagnosis.  The 
intellectual  child,  the  mature  child,  never  fails  to  grasp  the 
significance  of  the  test.  On  the  other  hand,  young  children  and 
the  immature  in  the  upper  ages  neglect  the  main  point  to  a 
great  extent.  In  clinical  cases  I  have  had  a  precocious  ten  year 
old  girl  draw  the  man  six  feet  in  height ;  while  a  badly  retarded 
girl  of  fifteen  drew  the  man  twenty-two  feet  in  height. 

Test  VII. 

Problems. 

This  test  is  in  reality  a  group  of  seven  problems,  designed 
to  test  the  judgment,  ingenuity,  and  inventive  ability  of  the 
child. 

Problem  1. — A  square  piece  of  cardboard,  72mm.  in  each 
dimension,  is  cut  into  four  equal  isosceles  triangles  along  the 
two  diagonals.  The  material  used  in  this  and  the  two  succeed- 
ing problems  is  a  high  grade  four-ply  card,  black  on  one  side, 
gray  on  the  other.  The  child  is  required  to  keep  the  black  side 
up.  The  child  is  given  the  four  triangles  and  requested  to  put 
them  together  so  that  they  will  look  like  the  model  (a  card  board 
of  the  original  size  and  form).  The  instructions  are,  "Put  these 
together  so  that  they  will  look  exactly  like  that/'  spoken  while 
placing  the  pieces  in  front  of  the  child. 


A  Graduated  Scale  for  Determining  Mental  Age         25 


Prob.    I. 


Prob.    II. 

Fig-.   10. 


Prob.    III. 


In  problems  1,  2  and  3,  the  time  required  for  the  solution 
was  taken  with  the  stop  watch  and  a  record  kept.  It  was  soon 
found  that  ability  was  not  directly  proportional  to  the  time 
required  and,  after  a  large  number  of  preliminary  tests,  the 
problem  was  counted  correct  if  solved  within  three  minutes. 
The  precocious  child  is  apt  to  put  the  pieces  together  quickly, 
but  a  child  who  slowly  and  deliberately,  after  repeated  trials, 
finally  reaches  a  solution  should  receive  full  credit. 

Problem  2. — A  rhombus,  whose  sides  were  each  72mm., 
angles  60°  and  120°,  was  cut  into  four  equal  right  triangles 
along  the  two  diagonals.  A  model  of  the  same  dimensions  was 
used.  The  entire  procedure  was  as  in  problem  1,  allowing  three 
minutes  for  a  solution. 

These  two  problems  are  similar  in  form  yet  present  contrast- 
ing difficulties.  In  the  first,  the  child  immediately  places  two 
triangles  together,  hypotenuse  against  hypotenuse,  forming  a 
square.  This  is  repeated  with  the  other  two  triangles  and  the 
whole  put  together  in  the  form  of  a  rectangle.  The  child  of  low 
mentality  usually  is  satisfied  with  this  rectanglar  form  and  is 
ready  for  the  next  test.  The  normal  child,  on  the  other  hand, 
breaks  up  the  form  and  tries  another  method.  The  procedure  in 
problem  two  is  to  form  a  symmetrical  figure  by  placing  two  tri- 
angles together  along  their  longest  side.  As  a  matter  of  fact, 
the  aesthetic  demand  for  symmetry  and  balance  asserts  itself 
in  all  ages  in  these  three  tests,  and  must  be  overcome  before  a 
solution  is  possible.  For  example,  the  children,  after  picking  up 
two  triangles,  will  habitually  put  them  together,  thus 


26         A  Graduated  Scale  for  Determining  Mental  Age 


Problem  3.* — A  rectangle  52mm.  x  80  mm.  is  cut  into 
three  triangles,  all  similar  but  unequal,  as  indicated  in  figure 
10.  The  method  is  the  same  as  that  used  in  the  two  preced- 
ing problems. 

In  case  of  failure,  we  pass  to  the  next  test  with  the  re- 
mark, "We'll  let  that  one  go  for  a  few  minutes.  Here's  an- 
other one  which  I  think  is  easier."  In  no  case  should  the  atten- 
tion of  the  child  be  drawn  to  a  lack  of  success.  The  effort  seemed 
to  be  constant,  and  usually  represented  the  maximum  of  the 
child's  ability.  In  several  instances,  after  finishing  these  three 
tests,  I  have  had  a  child  say,  "Yes,  but  I  want  to  try  that  other 
one  again.  I  believe  I  can  get  it  now." 

The  general  results  for  these  problems  are  given  in  the  fol- 
lowing table: 


Age 

6 

7 

8 

9 

10 
11 
12 
13 
14 


No.  Ch. 
40 
40 
41 
53 
42 
49 
40 
46 
53 


TABLE  XV. 

Problem  1  Problem  2 

No.    Ave.  Time      No.     Ave.  Time 
Correct   in  Sec.f    Correct   in  Sec. 


Problem  3 
No.    Ave.  Time 
Correct   in  Sec. 


8 
9 

17 
14 
20 
26 
20 
28 
36 


46 
63 
74 
66 
66 
67 
59 
72 
76 


11 
14 
15 
23 
23 
37 
30 
36 
45 


60 
81 
75 
81 
60 
65 
55 
70 
59 


2 
7 

13 
23 
23 
35 
23 
37 
37 


75 

60 
48 
74 
69 
66 
73 
70 
86 


Table  XVI.  gives  the  percentages  of  correct  solutions  of 
each  problem  for  each  age. 


Boys 

%  Solving 
Age        123 


TABLE  XVI. 

Girls 

%  Solving 
1.2          3 


Both 

%  Solving 
123 


6 

30 

35 

5 

7 

33 

61 

26 

8 

47 

47 

37 

9 

30 

41 

56 

10 

55 

60 

60 

11 

58 

79 

67 

12 

55 

87 

60 

13 

76 

84 

84 

14 

92 

80 

80 

5 

12 
41 
35 
50 

48 
50 
57 
93 


20 
18 
27 
46 
64 
72 
72 
76 
90 


6 

18 
31 
64 
72 
61 
76 
64 


18 
25 
44 
32 
53 
53 
53 
68 
93 


27 
43 
37 
44 
62 
76 
80 
80 
85 


5 

18 
27 
44 
62 
70 
35 
80 
72 


This  table  bears  me  out  in  the  method  used  in  evaluating 
the  results  of  these  three  problems.  Indicated  graphically  in 
figure  11,  we  may  infer  that  the  length  of  time  is  more  or  less 
irrelevant,  provided  three  minutes  is  the  limit. 

"Taken  from  Mrs.  Squire's  monograph  (22). 

fAve.  T.  is  the  average  time  of  those  who  actually  solved  the 
problems.  While  somewhat  irrelevant,  I  give  this  table  to  show  that, 
of  those  who  can  put  the  puzzles  together  within  the  time  limit,  there 
is  no  correlation  with  age.  In  fact,  we  may  say  that  the  average  time 
of  those  who  can  put  the  puzzles  together  within  three  minutes,  in- 
creases with  age.  I  suggest  this  explanation:  The  younger  children 
either  solve  it  at  once  or  reach  their  limit  of  ingenuity  after  the  first 
few  trials,  while  the  older  children  are  more  persistent,  a  larger  pro- 
portion solving  the  puzzle,  but  with  a  longer  average  time. 


A  Graduated  Scale  for  Determining  Mental  Age         27 


70 


I 


10 


t  --- 


9/00 

Fig:.  11. 


12       13       f* 


Problem  4. — This  is  the  paper  cutting  test  used  by  Binet  in 
his  1908  series.  A  sheet  of  note  book  paper  is  twice  folded  double 
in  the  presence  of  the  child,  and  the  corner  formed  by  the 
center  of  the  paper  is  cut-off,  forming  a  diamond  shaped  figure 
in  the  center.  The  child  is  required  to  draw  a  picture  of  the 
paper  showing  the  cut.  The  instructions  are  given  in  the  follow- 
ing sentence:  "I  fold  this  paper  over  like  this,  then  like  this, 
then  I  take  the  scissors  and  cut  off  that  corner.  Now  draw  a 
picture  of  the  paper  just  as  it  would  look  if  we  were  to,  open  it  and 
spread  it  flat  on  the  table."  The  cut  must  be  drawn  approxi- 
mately at  an  angle  of  forty-five  degrees  with  the  edges  to  pass 
as  correct.  That  is,  a  square  in  the  centre  of  the  paper  with  its 
sides  parallel  with  those  of  the  paper,  is  classified  as  a  failure. 

TABLE  XVII. 
First  Test  in  Paper  Cutting. 

Girls  Both 

0  0 

6  15 

31  31 

39  43 

55  55 

68  72 

84  78 

81  78 

93  91 

Problem  5. — The  Binet-Simon  clock  problem,  slightly  modi- 
fied, was  used  as  the  fifth  in  this  group.  The  problem  is  to  tell 
what  time  it  would  be  by  the  clock  if  the  hands  were  inter- 
changed when  it  is  (a)  nine  o'clock;  (b)  two  o'clock.  The  in- 
structions to  the  child  are  as  follows :  "Suppose  it  is  nine  o'clock 
by  the  watch  and  I  change  the  hands,  putting  the  big  one  where 
the  little  one  is,  and  the  little  one  where  the  big  one  is.  What 
time  would  it  be?"  This  was  repeated  for  the  second  part  using 
the  words  two  o'clock.  Full  credit  is  given  if  both  are  answered 
correctly,  half  credit  if  one  is  answered  correctly. 


Age 
6 

Boys 
0 

7 

8  .. 
q 

31 
48 

10 

55 

11 

86 

1? 

73 

13 

76 

14 

88 

28         A  Graduated  Scale  for  Determining  Mental  Age 


TABLE  XVIII. 
Interchanging  of  Hands  of  Clock  at  9  and  2. 


Age 

6  .. 

7  .. 

8  .. 

9  .. 

10  .. 

11  .. 

12  .. 

13  .. 

14  .. 


Boys 
% 
0 
0 

18 
43 
55 
91 
89 
94 
96 


Girls 
% 
0 
0 

14 
23 
59 
68 
86 
88 
97 


Both 


0 

16 
33 
57 
74 
88 
91 
96 


Problem  6. — This  is  the  reversed  triangle  used  by  Binet  in 
the  adult  series.  The  child  is  shown  two  equal  right  triangles 
so  placed  that  they  will  form  a  rectangle.  The  problem  is  to 
draw  the  two  triangles  as  they  would  appear  with  the  lower  one 
so  turned  that  line  A-B  would  be  against  line  C-D,  with  angle 


Fig.   12. 

B  joining  angle  D.  (Fig.  12.)  The  triangles  are  cut  from  a 
card  board  rectangle  82mm.  x  52  mm.  No  letters  or  marks  are 
allowed  on  the  triangle.  In  giving  the  exercise  the  triangles 
are  placed  on  the  table  before  the  child  with  the  explanation: 
"Imagine  the  lower  triangle  to  be  turned  around  so  that  this 
edge  (indicating  A-B),  is  placed  against  this  edge  (indicating 
C-D),  and  this  angle  (B),  against  this  angle  (D).  Draw  a 
picture  of  the  two  triangles  in  that  position."  If  the  child  does 
not  comprehend,  the  instructions  are  repeated.  Credit  is  allowed 
only  when  the  angles  are  properly  placed.  The  common  error 
in  this  problem  is  to  place  the  right  angle  in  the  middle  of  line 
C-D,  rather  than  at  point  D. 


Age 

6  .. 

7  .. 

8  .. 

9  .. 

10  .. 

11  .. 

12  .. 

13  .. 

14  .. 


TABLE  XIX. 
Rearranging  Two  Triangles. 


Boys 
% 
0 
0 

.       5 
0 

10 
0 

13 

.     32 
28 


Girls 

% 
0 
0 
5 
0 
5 
8 

17 
5 

32 


Both 
% 
0 
0 
5 
0 
7 
4 

15 
20 
30 


A  Graduated  Scale  for  Determining  Mental  Age         29 

Problem  7. — This  problem  is  also  taken  from  Binet,  being 
an  adult  test  in  the  1905  series.  While  giving  the  explanation 
the  experimenter  folds  a  rectangular  sheet  of  note  paper,  as  in 
problem  four;  the  cut  is  triangular,  made  in  the  side  which 
presents  a  single  fold.  The  subject  is  not  permitted  to  touch 
the  paper  and  must  not  fold  another  sheet.  Binet  says  of  this 


Fig.  13. 

problem:  "This  test  is  difficult.  Most  subjects  simplify  the 
solution  greatly.  They  think  that  only  one  hole  is  cut,  a  square 
or  a  diamond,  sometimes  a  five-pointed  star,  and  that  position  is 
in  the  center  of  the  paper."  (4>59)  To  be  correct  two  diamonds 
must  be  drawn  in  line  with  each  other  on  the  longest  diameter, 
one  in  the  upper,  the  other  in  the  lower  half.  If  the  diamonds 
are  drawn  on  the  shorter  diameter,  half  credit  is  allowed. 

TABLE   XX. 
Second   Paper  Cut. 

Boys  Girls  Both 

Age  %  %  % 

6  000 

7   000 

8  021 

9  11  2  7 

10  10  18  14 

11  40  36  38 

12  43  50  46 

13  44  66  54 

14  60  70  65 

The  seven  problems  given  in  test  VII.  are  grouped  together 
in  the  final  scale  and  treated  as  one,  hence  I  classify  them  in 
table  XXI.  in  the  same  manner  as  each  of  the  preceding  tests. 

It  may  be  mentioned  that  experience  soon  teaches  an  ex- 
perimenter that  it  is  useless  to  give  all  the  tests  in  this  group 
to  each  child.  Only  the  first  four  are  given  to  the  six  and  seven 
year  group.  Problem  five  cannot  be  given  to  a  child  who  is  un- 
able to  tell  time.  Problem  six  is  seldom  given  to  a  child  who 
is  apparently  running  below  twelve  in  mentality.  If  a  child 
shows  signs  of  precocity  he  is  given  each  one  of  the  group.  The 
rule  which  I  observed  throughout  was  to  give  the  test  if  there 
was  the  least  possibility  of  the  child's  passing  it. 


30 


A  Graduated  Scale  for  Determining  Mental  Age 


TABLE  XXI. 


Summary  of 

the 

Seven 

Tests 

in  Group  VII. 

BOYS 

GIRLS 

BOTH 

Age 

No. 

Total 

Av. 

M.  V. 

No. 

Total 

Av. 

M.  V. 

No. 

Total 

Av. 

M.  V 

6 

20 

14 

.7 

.56 

20 

6 

.3 

.48 

40 

20 

.5 

.6 

7 

23 

33 

1.43 

.84 

17 

7 

.4 

.56 

40 

40 

1.0 

.82 

8 

19 

35.5 

1.87 

1.03 

22 

30.5 

1.4 

1.10 

41 

66 

1.61 

1.08 

9 

27 

61.5 

2.28 

1.18 

26 

45.5 

1.8 

1.21 

53 

107 

2.02 

1.21 

10 

20 

61.0 

3.05 

.92 

22 

69.0 

3.14 

1.10 

42 

130 

3.10 

.97 

11 

24 

94.5 

3.94 

1.31 

25 

93.0 

3.7 

.97 

49 

187.5 

3.82 

1.09 

12 

22 

90.0 

4.09 

1.03 

18 

75.5 

4.2 

.74 

40 

165.5 

4.14 

.89 

13 

25 

122.5 

4.90 

1.00 

21 

94.5 

4.5 

.76 

46 

217.0 

4.72 

1.00 

14 

25 

131.0 

5.2i 

1.17 

28 

150.5 

5.4 

.87 

53 

218.5 

5.31 

.87 

See  lower  curve  Fig.  14  for  the  norm. 


t  . 

IX   _ 

j. 

^ 

'f 

/ 

& 

f 

is  — 

0 

/ 

S 

^ 

"& 

1    <?. 

S 

674 

9        /O      //       IZ       19  ~  M 
Fiff.  14. 

Test  VIII. 

Definitions. 

It  is  generally  agreed  that  ability  to  express  ideas  verbally  is 
a  good  criterion  of  intelligence.  In  the  search  for  a  test  which 
could  be  used  throughout  the  age  series  and  at  the  same  time 
parallel  the  genetic  development  of  the  child,  no  better  test  could 
be  found  than  a  series  of  definitions.  The  words  selected  fall 
into  three  groups,  as  follows:  (1)  Terms  used  in  the  every  day 
life  of  the  child,  fork,  horse  and  automobile;  (2)  Terms  which 
are  not  so  easily  classified  and  which  require  a  higher  type  of 
definition  than  is  usually  given  in  the  first  group,  poet  and  tree; 
(3)  Abstract  terms,  kindness,  sweetness,  charity  and  justice.  A 
tenth  was  added  under  this  heading,  namely,  the  difference  be- 
tween a  worm  and  a  snake. 

The  test  is  given  with  the  following  instructions:  "I  am  go- 
ing to  ask  you  several  questions.  Answer  them  the  very  best 
you  can.  First,  what  is  a  fork?" 

The  answers  for  the  present  purpose,  are  easily  classified 
in  three  groups: 

1.  Simple  repetition  or  silence.  The  common  response  for 
a  six-year-old  is  "Why,  a  fork  is  a  fork."  "A  horse  is  a  horse. " 
Children  of  this  type  use  the  same  response  for  fork,  horse. 


A  Graduated  Scale  for  Determining  Mental  Age         31 

automobile  and  tree  and,  as  one  would  expect,  make  no  response 
to  the  other  questions,  except  the  last  "What  is  the  difference 
betwen  a  worm  and  a  snake?"  the  answer,  "A  snake's  bigger," 

2.  Definitions  in  terms  of  use. — A  few  typical  examples: 
A  fork  is  a  thing  to  eat  with.  A  horse  is  to  ride  on,  or  to  pull 
carriages.  An  automobile  is  to  ride  in  or  carry  groceries  in.  A 
tree  is  to  get  fruit  off  of.  As  Binet  says,  "All  these  answers  are 
clearly  infantile,  not  only  in  their  incorrect  form,  but  also  in 
their  conciseness,  and  finally  in  the  state  of  mind  which  they 
reveal;  scarcely  any  children  of  seven   years    are    exclusively 
utilitarian  in  their  definitions.  "(4>28) 

3.  Definitions  in  terms  superior  to  use. — When  an  attempt 
is  made  to  give  a  more  elaborate  definition  the  answers  at  once 
become  much  more  diversified.  The  first  step  is  to  give  the  class, 
next  the  differentia.    The  type  of  answer  is  in  large  measure 
dependent  upon  the  degree  of  the  child's  familiarity  with  the 
object  being  defined.    The  lowest  class  in  this  type  is  that  in 
which  the  genus  is  given  followed  by  the  use.    The  real  value 
of  the  definition  depends,  of  course,  upon  the  number  of  dif- 
ferentia given,  and  the  classification.    In  this  group  horse  is 
defined    as,  an  animal;  a  beast  of  burden;  a  domestic  animal 
used  as  a  beast  of  burden. 

Method  of  Evaluating. — At  first  glance  the  problem  of 
evaluating  this  series  of  definitions,  so  that  it  may  be  used  in  a 
point  system,  may  seem  especially  difficult.  But  the  scale  which 
was  adopted  permits  an  accurate  evaluation  after  a  little  prac- 
tice. It  is,  briefly,  this:  For  each  definition,  allow  one  point  if 
in  terms  of  use  only.  If  the  proper  class  is  given  allow  one 
point.  For  each  differentium  allow  one  point.  With  the  one 
restriction — no  definition  shall  receive  more  than  three  points. 
In  the  tenth,  the  difference  between  a  worm  and  a  snake,  allow 
one-half  point  for  each  valid  difference. 

1.  Fork. — To  eat  with,  score  1.    Utensil  used  to  eat  with, 
score  2.  A  table  utensil  used  in  eating,  score  3. 

2.  Horse. — To  ride,  score  1.    Animal  to  ride  on,  score  2. 
Domestic  animal,  score  2.  Four-legged  animal,  score  1.  Domestic 
animal  used  for  hauling  wagons,  score  3. 

3.  Automobile. — To  ride  in,  score  1.    A  vehicle,  score  1. 
A  vehicle  to  ride  in,  score  2.   A  four-wheeled  vehicle,  score  1. 
A  thing  run  by  machinery,  score  1.  A  wagon  run  by  an  engine, 
or  a  self-propelled  vehicle,  score  3. 

4.  Poet. — Man  that  writes  poetry,  score   1.    (In  general 
tautological  definitions  do  not  receive  credit.    The  above,  how- 
ever, involves  a  higher  meaning  than  to  say  "A  poet  is  a  poet.") 
Man  who  ivrites  verses,  score  2.  Man  who  writes  stories  that 
rhyme,  score  3.    Man  that  writes  beautiful  thoughts  in  verse 
form,  score  3. 

5.  Tree. — A  thing  to  climb,  score  1.     Used   for    lumber, 
score  1.  To  get  fruit  off  of,  score  1.  A  plant,  score  1.  The  largest 
of  all  plants,  score  2.  A  big  piece  of  ivood  growing  in  the  ground, 
score  2.  A  large  plant,  with  big  trunk  and  branches,  used  for 
wood,  score  3. 

6.  Kindness. — To  be  kind,  no  credit.   Being  nice,  score  1. 


32         A  Graduated  Scale  for  Determining  Mental  Age 

Helping  others,  score  2.  To  be  polite,  unselfish  and  helpful  to 
others,  score  3. 

7.  Sweetness. — To   be  sweet,  no  credit.    Something    that 
tastes  like  sugar,  score  2.  A  taste,  score  1.   Like  kindness,  score 
1.  There  are  two  kinds;  something  that  tastes  like  sugar  and 
when  people  look  sweet  and  are  nice  to  one  another,  score  3. 
(Note — Perhaps  kindness  and  sweetness  should  have  been  re- 
versed. As  it  is,  the  idea  of  sweetness  being  like  kindness,  is  given 
oftener  than  was  anticipated.) 

8.  Charity. — Helping  others,  score  2.    Giving  help  to  the 
poor,  score  3.    (When  this  word  was  denned  at  all  the  answers 
were  similar  to  those  given.    In  the  main,  the  concept  was  con- 
crete rather  than  abstract.) 

9.  Justice. — To  be  just,  so  credit.    To  do  right,  score  2. 
To  do  unto  others  as  you  would  have  them  do  to  you,  score  3. 
//  a  person  is  in  jail  and  gets  what's  coming  to  him,  that's 
justice,  score  2. 

10.  Difference  between  a  worm  and    a    snake. — One-half 
point  for  each  difference.    Size,  form,  teeth,  skin,  head,  motion, 
bones,  feet,  color,  are  typical  differences  mentioned. 

In  evaluating  the  above  definitions  one  must  not  be  de- 
ceived by  a  high  sounding  phrase,  but  must  measure  the  ideas 
contained  in  the  phrase.  For  example,  children  occasionally 
respond  to,  "What  is  a  fork?"  with,  "A  fork  is  an  instrument 
used  to  convey  food  to  the  mouth."  This  does  not  necessarily 
indicate  a  higher  degree  of  intelligence;  it  is  more  likely  a  re- 
sult of  training. 

TABLE  XXII. 
Summary  of  Points  Made  in   Definition  Test. 


Bo 
Age             Av. 

69 

ys                                  Girls 
M.  V.                 Av.             M.  V. 
1.75                  3.4              1.8 
1.48                   4.15             1.36 
1.76                   4.95             1.05 
1.50                   6.13             1.66 
1.90                   8.32             2.58 
2.17                 10.62             1.80 
2.98                 11.36             2.14 
2.57                 13.48             2.52 
3.86                 15.40             2.91 

Both 
Av.           M.  V. 
3.20            1.86 
4.29            1.45 
5.58             1.49 
6.75             1.64 
7.70             2.52 
11.17             2.02 
12.40             2.80 
13.82             2.56 
15.35            3.16 

J 

2. 

1 

74  4 

ft                        co 

97  4 

10  7.1 

n-l  I    Q 

10                                 I  0   OC 

13  14.12 

HI  Z   0 

/£> 

„</ 

it 

*»*; 

^ 

Y 

f 

1  //> 

/ 

!/ 

& 

V 

cgfi 
*6 

N  4" 
2. 

1 

/ 

*''/, 

^ 

$ 

/ 

/ 

j    * 

X 

/ 

f 

/ 
// 

•\. 

^ 

^ 

** 

m,              • 

^^ 
/ 

^ 

5       7       6       9       10      II       12,      /3      14- 
Pigr.  15. 

A  Graduated  Scale  for  Determining  Mental  Age         33 

Test  IX. 

Sorting  Cards. 

For  this  test  a  set  of  fifty  cards  is  employed  utilizing  the 
rather  complex  function  of  discrimination  of  form  and  color. 
The  cards  used  are  of  highest  grade  duplex  calling  card  stock, 
in  size  the  same  as  an  ordinary  playing  card,  63x89mm.  Spots 
are  arranged  as  shown  in  figure  16,  forming  five  sets  of  ten 
cards  each.  Colors  used  are  blue,  green  and  red;  forms  are 
circle,  10%  mm.  in  diameter,  a  square  9  mm.  each  side,  and  an 
equilateral  triangle  each  of  whose  sides  is  14  mm.  (Area  of 
spots  practically  equal.)  The  cards  are  sized  with  collodion  as 
a  protection  to  the  colors. 

In  all  sets  the  colors  are  retained  in  the  same  order,  namely, 
blue  at  the  top,  green  in  the  middle,  and  red  at  the  bottom.* 


Fig:.   16. 

After  carefully  shuffling  the  cards  they  are  shown  to  the 
student  with  the  explanation,  "Now  I  want  you  to  sort  these 
cards  for  me.  I'll  show  you  the  different  kinds  there  are.  This 
one,  and  this  one,  etc.  Now  you  are  to  sort  them  over,  putting 
the  ones  that  are  just  alike  in  the  same  piles.  Do  you  see  how  they 
are  all  different?"  In  the  meantime  the  experimenter  may  be 
shuffling  the  cards  allowing  sufficient  time — about  one  minute — 
for  the  child  to  discover  the  fundamental  differences  in  the  five 
sets.  Then  gathering  up  the  five  sample  cards,  place  them 


*Sets  may  be  secured  by  communicating  with  the  author. 


34         A  Graduated  Scale  for  Determining  Mental  Age 

at  the  bottom  of  the  deck  and  hand  all  to  the  child  with  the  re- 
mark: "//  you  find  a  card  and  have  no  place  to  put  it,  start  a 
new  pile.  Just  as  quickly  as  you  can  now,  but  don't  make  any 
mistakes."  A  record  is  kept  of  the  time  in  minutes  and  sec- 
onds, with  the  number  of  errors. 

In  this  test  care  should  be  taken  to  see  that  the  child  under- 
stands the  problem  thoroughly.  The  differences  in  the  cards 
should  not  be  explained,  but,  in  the  cases  of  slower  children,  a 
little  longer  time  may  be  allowed  in  looking  at  the  cards  at 
first.  The  common  type  of  error  is  to  place  the  two  sets  which 
have  circles  at  the  top  in  the  same  pile.  Cards  must  not  be  in- 
verted. 

As  a  means  of  quickly  detecting  mistakes  in  piling,  the  set 
number — 1,  2,  3,  4,  or  5— is  placed  on  the  back  in  the  upper 
left  hand  corner.  An  error  is  counted  each  time  a  new  number 
appears  in  the  course  of  running  them  through.  That  is,  sup- 
pose set  4  checks  as  follows:  4-4-4-3-4-2-2-2-4-2.  We  have  here 
five  errors — one  when  card  3  was  placed  on  card  4,  one  when 
card  4  was  placed  on  card  3,  one  when  card  2  was  placed  on  card 
4,  etc.  The  theory  being  that  each  time  a  wrong  card  is  placed 
on  a  pile  the  pile  takes  the  individuality  of  the  new  card,  and 
adding  any  other  card  than  the  new  will  constitute  an  error. 

Count  is  also  taken  of  the  number  of  piles.  Usually  there 
are  more  errors  than  extra  piles,  but  if  this  is  not  the  case,  each 
extra  pile  above  the  number  of  errors  constitutes  an  error. 

In  tabulating  results  I  was  unable  to  find  any  particular 
degree  of  correlation  between  accuracy  and  speed,  except  in  in- 
dividual cases.  To  analyze  this  factor  would  necessitate  taking 
each  age  as  a  group  and  evaluating  the  correlation.  There  are 
indications  of  such  a  correlation,  especially  in  the  older  groups. 

In  the  following  table  seconds  have  been  changed  to  frac- 
tions of  a  minute  for  convenience. 

TABLE  XXIII. 
Card   Sorting  Test. 

Boys  Girls  Both 

Age        Av.              M.V.  Av.  M.  V.  Av.  M.V. 

6 6.27  1.23  6.79  1.33  6.53  1.28 

7 5.73  .73  4.88  .90  5.37  .84 

8 5.29  .91  4.50  .70  4.86  .86 

9 4.45  .62  4.54  .95  4.50  .77 

10 4.36  .70  3.76  .78  4.05  .79 

11 3.62  .73  3.48  .52  3.56  .65 

12 3.79  .69  3.03  .43  3.45  .64 

13 3.45  .82  2.84  .47  3.17  .73 

14 3.13  .67  3.09  .49  3.10  .61 

In  this  test  the  girls  are  slower  than  the  boys  except  at 
the  ages  six,  nine  and  fourteen.  The  girls'  greatest  variation 
comes  at  the  point  where  they  make  their  greatest  gain — year 
seven.  The  greatest  increase  in  speed  is  prior  to  year  eleven.  But 
little  increase  (3.56  min.  to  3.10  min.)  is  apparent  from  eleven 
to  twelve.  (See  Fig.  17,  upper  curve.) 


A  Graduated  Scale  for  Determining  Mental  Age         35 


51 


I 


3       10       n 
Fig.  17. 


14- 


TABLE  XXIV. 
Average  Number  of  Errors  Made  in  Sorting  Cards. 


Boys 
Girls 
Both 


6 

6.2 
6.1 
6.1 


7 

4.4 
4.4 
4.4 


8 

•  5.7 
5.4 
5.6 


9 

5.0 
5.3 
5.2 


10 
5.1 

4.8 
4.9 


11 
6.0 
4.9 
5.5 


12 
4.8 
5.0 
4.9 


13  14 

5.2  4.8 

5.0  4.1 

5.1  4.4 


In  practice,  and  in  evaluating  the  number  of  points  for 
this  test  (see  next  paragraph).  I  add  to  the  actual  time,  an  addi- 
tional time  of  three  seconds  for  each  error. 

Evaluation  of  Points  for  the  Graduated  Scale. 

The  assigning  of  weight  to  each  of  the  several  tests  is 
necessarily  an  arbitrary  matter.  The  ideal  would  be  to  give 
equal  weight  to  the  various  mental  processes  if  they  could  be 
labeled  and  tested.  But  that  being  impossible,  effort  was  made  to 
distribute  the  weights  to  the  various  tests  in  a  manner  which 
would  facilitate,  rather  than  hinder  the  task  of  evaluating  the 
material,  while  at  the  same  time  distributing  the  points  so  that 
the  increase  from  year  to  year  would  be  as  large  as  possible. 

Test  I. — Allow  one  point  for  each  object  enumerated. 

Test  II. — Allow  one  point  for  each  digit. 

Test  III. — Divide  number  of  syllables  by  4.  (This  gives 
auditory  memory  for  syllables  the  same  weight  as  auditory  mem- 
ory for  digits.)'  (See  table  XXV.) 

Test  IV. — Allow  two  points  for  each  figure  correctly  drawn. 

Test  V. — Divide  total  number  words  given  by  3. 

Test  VI. — Number  of  points  allowed  is  obtained  by  divid- 
ing 100  by  the  height  of  the  man. 

Test  VII. — Multiply  points  made  in  the  seven  problems  by 
3. 

Test  VIII. — Allow  one  point  for  each  score  as  indicated  in 
the  description  of  this  test. 

Test  IX. — Divide  30  by  the  time  taken  in  sorting  the  cards 
recorded  in  minutes. 


36         A  Graduated  Scale  for  Determining  Mental  Age 

In  the  summation  of  points  boys  are  higher  than  girls 
except  at  year  ten  and  the  curves  will  probably  cross  soon  after 
year  fourteen.  (See  tables  XXV.  and  XXVI.) 


TABLE  XXV. 
Summation  of  Points  for  Boys. 


Test 

6 

7 

8 

9 

10 

11 

12 

13 

14 

1 

3.3 

4.2 

4.3 

5.0 

5.0 

5.8 

5.6 

5.9 

6.1 

2 

4.3 

5.0 

5.4 

5.7 

5.7 

5.8 

6.0 

6.1 

6.4 

3 

3.9 

4.1 

4.3 

4.6 

4.4 

5.6 

5.6 

5.9 

6.1 

4 

4.0 

5.6 

7.0 

9.2 

8.6 

11.4 

11.8 

13.6 

16.2 

5 

4.5 

4.7 

6.1 

7.7 

7.5 

9.8 

10.0 

10.3 

10.3 

6 

5.2 

5.2 

4.8 

6.3 

6.1 

6.6 

10.2 

8.3 

8.7 

7 

2.1 

4.3 

5.6 

6.8 

9.2 

11.8 

12.3 

14.7 

15.7 

8 

3.0 

4.4 

6.3 

7.4 

7.1 

11.8 

13.3 

14.1 

15.3 

9 

4.6 

5.0 

5.4 

6.4 

6.4 

7.8 

7.4 

8.1 

8.9 

34.2        42.5        49.2        59.0         60.0        76.4         82.1         87.0 


93.7 


TABLE  XXVI. 
Summation  of  Points  for  Girls. 


Test 

6 

7 

8 

9 

10 

11 

12 

13 

14 

1 

3.3 

4.2 

4.4 

4.7 

5.0 

5.6 

5.9 

6.3 

6.6 

2 

4.5 

4.9 

5.6 

5.6 

5.5 

5.8 

6.0 

6.0 

6.3 

3 

4.0 

4.0 

4.3 

4.5 

4.6 

4.7 

5.5 

5.3 

5.9 

4 

3.2 

4.6 

6.2 

6.0 

9.0 

9.8 

10.4 

13.4 

14.0 

5 

3.9 

4.7 

5.8 

7.1 

7.3 

8.5 

11.6 

9.6 

11.0 

6 

4.5 

4.1 

6.2 

4.9 

4.9 

7.3 

5.9 

7.2 

8.5 

7 

.9 

1.2 

4.2 

5.4 

9.4 

11.1 

12.6 

13.5 

16.2 

8 

3.4 

4.2 

5.0 

6.1 

8.3 

10.6 

11.4 

13.5 

15.4 

9 

4.2 

5.9 

6.3 

6.3 

7.5 

8.0 

9.2 

9.7 

9.1 

31.9        37.7        48.0         50.6         61.5         71.5         78.5         84.4 


93.0 


For  all   purposes  of   classification,   however,   the  two   are 
combined  giving  the  following: 


33.3 


TABLE  XXVII. 


Summation  of  Points  (See  Fig  18.) 


Test 

6 

7 

8 

9 

10 

11 

12 

13 

14 

1 

3.3 

4.2 

4.3 

4.9 

5.0 

5.7 

5.7 

6.1 

6.4 

2 

4.4 

4.9 

5.5 

5.7 

5.6 

5.8 

6.0 

6.1 

6.4 

3 

3.9 

4.0 

4.3 

4.5 

4.5 

4.7 

5.1 

5.6 

6.0 

4 

3.6 

5.2 

6.6 

8.0 

8.8 

10.6 

11.2 

13.6 

15.0 

5 

4.2 

4.7 

5.9 

7.4 

7.4 

9.1 

10.7 

10.0 

10.7 

6 

4.8 

4.7 

5.5 

5.5 

5.4 

6.9 

7.8 

7.8 

8.6 

7 

1.5 

3.0 

4.8 

6.0 

9.3 

11.4 

12.4 

14.1 

15.9 

8 

3.2 

4.3 

5.6 

6.8 

7.7 

11.2 

12.4 

13.8 

15.4 

9 

4.4 

5.4 

6.8 

6.3 

7.0 

7.9 

8.1 

8.8 

9.0 

40.0 


48.8         55.1 


60.6 


73.3 


79.4 


85.9         93.4 


A  Graduated  Scale  for  Determining  Mental  Age         37 


60 

V 


673 


9        /o        II 

18. 


O 


38         A  Graduated  Scale  for  Determining  Mental  Age 

By  use  of  interpolation  the  following  table  has  been  con- 
structed from  the  norms  given  above  and  serves  the  purpose  of 
quickly  estimating  the  ages  to  a  tenth  of  a  year. 

Table  XXVIII. 


No. 

Ment. 

No. 

Ment. 

No. 

Ment. 

No. 

Ment. 

Points 

Age 

Points 

Age 

Points 

Age 

Points 

Age 

33.3 

6.0 

48.4 

8.0 

60.6 

10.0 

79.4 

12.0 

34.0 

6.1 

49.1 

8.1 

61.9 

10.1 

80.1 

12.1 

34.7 

€.2 

49.7 

8.2 

63.1 

10.2 

80.7 

12.2 

35.4 

6.3 

50.4 

8.3 

64.4 

10.3 

81.4 

12.3 

36.1 

6.4 

51.1 

8.4 

65.7 

10.4 

82.0 

12.4 

36.9 

6.5 

51.8 

8.5 

67.0 

10.5 

82.7 

12.5 

37.6 

6.6 

52.4 

8.6 

68.2 

10.6 

83.3 

12.6 

38.3 

6.7 

53.1 

8.7 

69.5 

10.7 

84.0 

12.7 

39.0 

6.8 

53.8 

8.8 

70.8 

10.8 

84.6 

12.8 

39.7 

6.9 

54.4 

8.9 

72.0 

10.9 

85.3 

12.9 

40.4 

7.0 

55.1 

9.0 

73.3 

11.0 

85.9 

13.0 

41.2 

7.1 

55.7 

9.1 

73.9 

11.1 

86.7 

13.1 

42.0 

7.2 

56.2 

9.2 

74.5 

11.2 

87.4 

13.2 

42.8 

7.3 

56.8 

9.3 

75.1 

11.3 

88.2 

13.3 

43.6 

7.4 

57.3 

9.4 

75.7 

11.4 

88.9 

13.4 

44.4 

7.5 

57.9 

9.5 

76.4 

11.5 

89.7 

13.5 

45.2 

7.6 

58.4 

9.6 

77.0 

11.6 

90.4 

13.6 

46.0 

7.7 

59.0 

9.7 

77.6 

11.7 

91.2 

13.7 

46.8 

7.8 

59.5 

9.8 

78.2 

11.8 

91.9 

13.8 

47.6 

7.9 

60.1 

9.9 

78.8 

11.9 

9'2.7 

13.9 

BE:,      ! 

93.4 

14.0 

In  illustration  of  the  use  of  the  scale  I  shall  add  a  few 
actual  cases,  selected  at  random  from  among  those  which  were 
given  for  special  reasons. 

(1)  R.  W.,  a  girl,  age  10  years,  1  month,  seven  days; 
5A  grade.  Points  made  for  each  test  are,  respectively,  5.7,  5.5, 
11,  8.6,  7.1, 15, 10,  8.1,  a  total  of  77.3.  Referring  to  table  XXVII., 
the  mental  age  is  found  to  be  11.65  years,  showing  an  accelera- 
tion of  1.5  years. 

(2)  J.  B.,  a  boy,  age  13  years,  2  months,  17  days;  7A 
grade.    Points  made,  5,  5,  5,  23,  8.3,  4.2,  15,  12,  9.2,  total  86.7. 
Mental  age  13.1,  which  is  identical  with  the  chronological  age. 

(3)  R.  C.,  a  girl,  age  11  years,  4  months,  16  days;  3B 
grade.  Points  made  3,  6,  5,  4,  7.6,  7,  1.5,  9,  4.8,  total  47.9.  Mental 
age,  7.9,  which  is  3.4  years  below  her  chronological  age. 

(4)  C.  G.,  a  boy,  age  10  years,  1  month ;  4 A  grade.  Points 
made,  5,  7,  6,  17,  6.6,  8.7,  18,  11,  7.5,  a  total  of  86.8.  Mental  age 
13.1,  which  is  3  years  in  advance  of  his  chronological  age. 

The  list  could  be  extended  indefinitely  from  the  data  at 
hand,  but  no  attempt  has  been  made  to  summarize  the  work 
with  these  special  cases,  hence  I  submit  merely  the  above  in 
illustration  of  the  use  of  the  scale. 

Conclusion. 

After  using  the  scale  in  testing  between  five  and  six  hundred 
children  I  have  become  firmly  convinced  of  its  applicability  as 
an  instrument  for  "first  aid"  purposes.  Indeed,  its  results  are 
sufficient  to  classify  satisfactorily  the  majority  of  cases. 
Throughout  the  work,  I  repeatedly  compared  notes  with  the 


A  Graduated  Scale  for  Determining  Mental  Age          39 

teacher  and  principal,  and  practically  without  exception,  found 
that  my  estimate  of  the  child  corresponded  with  that  of  the  in- 
structor. At  each  school  which  I  visited  I  was  requested  to 
examine  special  cases,  with  the  result  that  the  scale  was  thor- 
oughly tried  out.  When  examining  children  at  the  request  of 
the  teacher  or  principal  I  made  it  a  rule  to  take  the  case  as  an 
"unknown."  With  very  few  exceptions  my  findings  were  cor- 
roborated by  the  facts  as  shown  by  class  standing  and  the  esti- 
mate of  the  teacher.  In  many  cases  I  have  pointed  out  individ- 
ual peculiarities  which  had  passed  unnoticed,  but  which  were  at 
once  recognized  when  the  teacher's  attention  was  directed  to- 
ward them.  A  glaring  example  came  to  light  one  day  while  I 
was  testing  children  for  special  promotion.  A  boy  of  twelve 
in  the  sixth  grade  had  been  recommended  as  a  candidate  but, 
owing  to  his  retiring  disposition,  his  teachers  were  not  convinced 
that  he  would  be  able  to  carry  the  advanced  work.  I  found 
that  he  was  mentally  about  four  years  in  advance  of  his  age — 
entirely  beyond  the  range  of  my  scale — and  capable  of  carrying 
high  school  work.  Even  his  mother  was  forced  to  admit  that, 
even  though  L —  -  was  not  considered  precocious,  she  always 
appealed  to  him  as  a  court  of  last  resort,  when  special  informa- 
tion was  wanted.  As  a  result  of  my  findings  he  was  advanced 
one  grade  and  placed  in  the  special  preparatory  school. 

This  confidence  in  the  scale  prompts  me  to  make  the  state- 
ment that  it  can  be  used  by  teachers  and  supervisors  with  grati- 
fying results.  With  its  application  one  can  ascertain  more  in 
thirty  minutes  concerning  the  actual  mental  condition  of  the 
child  than  is  ordinarily  possible  from  two  years  of  regular 
school  work.  Moreover  its  compactness  and  simplicity  of  opera- 
tion commend  it  especially  to  teachers  who  lack  a  complete 
training  in  experimental  pedagogy. 

There  is  no  question  but  that  such  a  measuring  instrument 
may  be  used  greatly  to  increase  the  efficiency  of  any  school 
system.  There  should  be  several  scales  available  but  all  of  a 
type  which  would  commend  their  use  to  the  rank  and  file  of  the 
teaching  profession.  Only  by  a  conscientious  effort  in  classi- 
fication will  the  schools  of  America  be  able  to  reach  the  standard 
which  the  public  has  a  right  to  demand  of  them — the  standard 
which  gives  each  individual  child  the  most  efficient  education  of 
which  he  is  capable. 

Bibliography.* 

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*No  attempt  is  here  made  to  compile  a  complete  bibliography. 
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40         A  Graduated  Scale  for  Determining  Mental  Age 

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A  Graduated  Scale  for  Determining  Mental  Age         41 

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